basic math formulae for students

list of important math formulae for students of class 10 and cbse ncert and stateboards like

identitites , surds, indices, quadratic equations, complex numbers, progressions like AP ,GP, HP

sum of the first n natural numbers, sum of their squares and their cubes, Analytical geometry like coordinate,

straight line, circle etc

important formula list for math students of class 10, class 11 class12 of cbse ncert isc and state boards

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Important results on how to handle indices and surds, some important algebraic identities

Indices, surd, algebraic identity

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roots of quadratic equation,formula to find the root of the quadratic equation,

relation between roots and coefficient of the quadratic equation, nature of the root using discriminant

Quadratic equation

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Complex number, concept of the imaginary unit i, powers of i, real and imaginary parts of

a complex number, modulus amplitude form

Complex number

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Arithmetic progression (AP), Geometric progression (G.P),

sum of the first n natural numbers, sum of the squares and cubes of the first n natural numbers

Arithmetic progression (AP), Geometric progression (G.P)

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distance between two points, section formula, midpoint formula, equation of

straight line , point slope,two point, intercept form,
equation of circle, condition

for orthogonal circle, equation of tangent to a circle are
given.

co ordinate, straight line , circle

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# mixture

## Wednesday, April 26, 2017

## Tuesday, March 14, 2017

### integral of [e^2x]cos3x using integration by parts

integral of [e^2x]cos3x using integration by parts

Take the integral as I

take cos3x as the first function and apply integration by parts , simplify and then apply integration by parts to the integral obtained in the first answer.

Simplify to get the original integral I in the right hand side and change it to I

Solve for I from this equation

formulae on integration

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PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

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PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

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Take the integral as I

take cos3x as the first function and apply integration by parts , simplify and then apply integration by parts to the integral obtained in the first answer.

Simplify to get the original integral I in the right hand side and change it to I

Solve for I from this equation

formulae on integration

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PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

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## Sunday, February 5, 2017

### linear differential equation y dx + [x-(y^2)]dy = 0

linear differential equation from ncert cbse

solve y dx + [x-(y^2)]dy = 0

The equation contains only one x term

Therefore try to solve for [dx/dy] and compare with the linear differential equation of the form

[dx/dy] + Px = Q

Then compare and get the values of P and Q

find the integrating factor of the linear differential equation using the formula

I.F. = e^[integral of P dx]

use the property e^[ln[f(y)] = f(y)

then use the solution

x[I.F.] = integral of [ Q * I.F.]dy +C

sinx cosy dx + cosx siny dy =0

solution of variable separable differential equation find the equation of the curve passing through (0,pi/4) whose differential equation issinx cosy dx + cosx siny dy =0

* show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0

is given by x+y+1=A[1-x-y-2xy]

*solve y e^(x/y) = [ y e^(x/y) + (y^2) ]dy [ y is not equal to 0]

solution of differential equation which is not homogeneous but which can be solved using x=vy

solution of linear differential equation of ncert cbse miscellaneous differential equation

*linear differential equation of the type

solve y dx + [x-(y^2)]dy = 0

solution of linear differential equation of the type [dx/dy] + Px = Q

*find a particular solution of the differential equation [dy/dx]+ycotx =4xcosecx [x is not 0] given that y =0 if x=pi/2

solution of linear differential equation from ncert cbse miscellaneous [dy/dx]+ycotx =4xcosecx [x is not 0] given that y =0 if x=pi/2

solution of a second order differential equation using reduction of order

solve y"-y = 0 if y = coshx is one of the solutions

using the formula for reduction of order

solution of solution of a second order differential equation using reduction of order

solution to problem on differential questions using variation of parameter method

answer to problem on orthogonal trajectory of y(1+x ² ) = Cx

solution to find the orthogonal trajectory of y = (k/x)

formulae on integration

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

solve y dx + [x-(y^2)]dy = 0

The equation contains only one x term

Therefore try to solve for [dx/dy] and compare with the linear differential equation of the form

[dx/dy] + Px = Q

Then compare and get the values of P and Q

find the integrating factor of the linear differential equation using the formula

I.F. = e^[integral of P dx]

use the property e^[ln[f(y)] = f(y)

then use the solution

x[I.F.] = integral of [ Q * I.F.]dy +C

Variable separable differential equation

*find the equation of the curve passing through (0,pi/4) whose differential equation issinx cosy dx + cosx siny dy =0

solution of variable separable differential equation find the equation of the curve passing through (0,pi/4) whose differential equation issinx cosy dx + cosx siny dy =0

* show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0

is given by x+y+1=A[1-x-y-2xy]

solution of differential equation which is not homogeneous but which can be solved using x=vy

*linear differential equation

solve [ { e^[-2sqrt(x)] / sqrt(x) } - {y / sqrt(x)}] [dx/dy] = 1 [x is not 0]solution of linear differential equation of ncert cbse miscellaneous differential equation

*linear differential equation of the type

solve y dx + [x-(y^2)]dy = 0

solution of linear differential equation of the type [dx/dy] + Px = Q

*find a particular solution of the differential equation [dy/dx]+ycotx =4xcosecx [x is not 0] given that y =0 if x=pi/2

solution of linear differential equation from ncert cbse miscellaneous [dy/dx]+ycotx =4xcosecx [x is not 0] given that y =0 if x=pi/2

solution of a second order differential equation using reduction of order

solve y"-y = 0 if y = coshx is one of the solutions

using the formula for reduction of order

solution of solution of a second order differential equation using reduction of order

### variation of parameter method

solve xy" - 4y' = x^4 by method of variation of parametersolution to problem on differential questions using variation of parameter method

### orthogonal trajectory of y(1+x ² ) = Cx

find the orthogonal trajectory of y(1+x ² ) = Cxanswer to problem on orthogonal trajectory of y(1+x ² ) = Cx

### orthogonal trajectory of y = (k/x)

find the orthogonal trajectory of y = (k/x)solution to find the orthogonal trajectory of y = (k/x)

formulae on integration

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

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There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

## Wednesday, February 1, 2017

### linear differential equation

linear differential equation from ncert cbse miscellaneous differential equation

find a particular solution of the differential equation [dy/dx]+ycotx =4xcosecx [x is not 0] given that y =0 if x=pi/2

the equation is an example of linear differential equation, so compare [dy/dx]+ycotx =4xcosecx with the standard linear differential equation [dy/dx]+Pycotx =Q

Identify the values of P and Q

here P=cotx

Q=4xcosecx

Find the integrating factor[I.F.] = e^[integral of P ]

use the result e^[ln{f(x)}] = f(x)

use the solution

y[I.F.] = integral of [ Q* I.F. ] +C

sinx cosy dx + cosx siny dy =0

solution of variable separable differential equation find the equation of the curve passing through (0,pi/4) whose differential equation issinx cosy dx + cosx siny dy =0

* show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0

is given by x+y+1=A[1-x-y-2xy]

*solve y e^(x/y) = [ y e^(x/y) + (y^2) ]dy [ y is not equal to 0]

solution of differential equation which is not homogeneous but which can be solved using x=vy

solution of linear differential equation of ncert cbse miscellaneous differential equation

solution of a second order differential equation using reduction of order

solve y"-y = 0 if y = coshx is one of the solutions

using the formula for reduction of order

solution of solution of a second order differential equation using reduction of order

solution to problem on differential questions using variation of parameter method

answer to problem on orthogonal trajectory of y(1+x ² ) = Cx

solution to find the orthogonal trajectory of y = (k/x)

formulae on integration

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

find a particular solution of the differential equation [dy/dx]+ycotx =4xcosecx [x is not 0] given that y =0 if x=pi/2

the equation is an example of linear differential equation, so compare [dy/dx]+ycotx =4xcosecx with the standard linear differential equation [dy/dx]+Pycotx =Q

Identify the values of P and Q

here P=cotx

Q=4xcosecx

Find the integrating factor[I.F.] = e^[integral of P ]

use the result e^[ln{f(x)}] = f(x)

use the solution

y[I.F.] = integral of [ Q* I.F. ] +C

Variable separable differential equation

*find the equation of the curve passing through (0,pi/4) whose differential equation issinx cosy dx + cosx siny dy =0

solution of variable separable differential equation find the equation of the curve passing through (0,pi/4) whose differential equation issinx cosy dx + cosx siny dy =0

* show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0

is given by x+y+1=A[1-x-y-2xy]

solution of differential equation which is not homogeneous but which can be solved using x=vy

*linear differential equation

solve [ { e^[-2sqrt(x)] / sqrt(x) } - {y / sqrt(x)}] [dx/dy] = 1 [x is not 0]solution of linear differential equation of ncert cbse miscellaneous differential equation

solution of a second order differential equation using reduction of order

solve y"-y = 0 if y = coshx is one of the solutions

using the formula for reduction of order

solution of solution of a second order differential equation using reduction of order

### variation of parameter method

solve xy" - 4y' = x^4 by method of variation of parametersolution to problem on differential questions using variation of parameter method

### orthogonal trajectory of y(1+x ² ) = Cx

find the orthogonal trajectory of y(1+x ² ) = Cxanswer to problem on orthogonal trajectory of y(1+x ² ) = Cx

### orthogonal trajectory of y = (k/x)

find the orthogonal trajectory of y = (k/x)solution to find the orthogonal trajectory of y = (k/x)

formulae on integration

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

## Tuesday, January 31, 2017

### linear differential equation for cbse ncert miscellaneous problem

linear differential equation for cbse ncert miscellaneous problem

solve [ { e^[-2sqrt(x)] / sqrt(x) } - {y / sqrt(x)}] [dx/dy] = 1 [x is not 0]

here there is only one term in y

so we have to rearrange the equation in the form

[dy/dx] + Py = Q

identify the values of P and Q

find the integrating factor e^[integral of P]

and use in the solution

y[integrating factor] = integral of [Q*integrating factor] + C

sinx cosy dx + cosx siny dy =0

solution of variable separable differential equation find the equation of the curve passing through (0,pi/4) whose differential equation issinx cosy dx + cosx siny dy =0

* show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0

is given by x+y+1=A[1-x-y-2xy]

*solve y e^(x/y) = [ y e^(x/y) + (y^2) ]dy [ y is not equal to 0]

solution of differential equation which is not homogeneous but which can be solved using x=vy

solution of a second order differential equation using reduction of order

solve y"-y = 0 if y = coshx is one of the solutions

using the formula for reduction of order

solution of solution of a second order differential equation using reduction of order

solution to problem on differential questions using variation of parameter method

answer to problem on orthogonal trajectory of y(1+x ² ) = Cx

solution to find the orthogonal trajectory of y = (k/x)

formulae on integration

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

solve [ { e^[-2sqrt(x)] / sqrt(x) } - {y / sqrt(x)}] [dx/dy] = 1 [x is not 0]

here there is only one term in y

so we have to rearrange the equation in the form

[dy/dx] + Py = Q

identify the values of P and Q

find the integrating factor e^[integral of P]

and use in the solution

y[integrating factor] = integral of [Q*integrating factor] + C

Variable separable differential equation

*find the equation of the curve passing through (0,pi/4) whose differential equation issinx cosy dx + cosx siny dy =0

solution of variable separable differential equation find the equation of the curve passing through (0,pi/4) whose differential equation issinx cosy dx + cosx siny dy =0

* show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0

is given by x+y+1=A[1-x-y-2xy]

solution of differential equation which is not homogeneous but which can be solved using x=vy

solution of a second order differential equation using reduction of order

solve y"-y = 0 if y = coshx is one of the solutions

using the formula for reduction of order

solution of solution of a second order differential equation using reduction of order

### variation of parameter method

solve xy" - 4y' = x^4 by method of variation of parametersolution to problem on differential questions using variation of parameter method

### orthogonal trajectory of y(1+x ² ) = Cx

find the orthogonal trajectory of y(1+x ² ) = Cxanswer to problem on orthogonal trajectory of y(1+x ² ) = Cx

### orthogonal trajectory of y = (k/x)

find the orthogonal trajectory of y = (k/x)solution to find the orthogonal trajectory of y = (k/x)

formulae on integration

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

### non homogeneous equation with the substitution x=vy

miscellaneous problem from ncert differential equation where the substitution x=vy still works even though is not a homogeneous equation

solve y e^(x/y) = [ y e^(x/y) + (y^2) ]dy [ y is not equal to 0]

here there are terms containing [x/y]

so extract dx/dy call the value of dx/dy as f[x,y]

replace x with tx and y with ty and check if the function is homogeneous

here f[tx,ty] is not equal to f[x,y]

therefore the function is not homogeneous

but the substitution v =(x/y) will still work for this problem

* show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0

is given by x+y+1=A[1-x-y-2xy]

solution of a second order differential equation using reduction of order

solve y"-y = 0 if y = coshx is one of the solutions

using the formula for reduction of order

solution of solution of a second order differential equation using reduction of order

solution to problem on differential questions using variation of parameter method

answer to problem on orthogonal trajectory of y(1+x ² ) = Cx

solution to find the orthogonal trajectory of y = (k/x)

formulae on integration

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

solve y e^(x/y) = [ y e^(x/y) + (y^2) ]dy [ y is not equal to 0]

here there are terms containing [x/y]

so extract dx/dy call the value of dx/dy as f[x,y]

replace x with tx and y with ty and check if the function is homogeneous

here f[tx,ty] is not equal to f[x,y]

therefore the function is not homogeneous

but the substitution v =(x/y) will still work for this problem

Variable separable differential equation

* show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0

is given by x+y+1=A[1-x-y-2xy]

solve y"-y = 0 if y = coshx is one of the solutions

using the formula for reduction of order

solution of solution of a second order differential equation using reduction of order

### variation of parameter method

solve xy" - 4y' = x^4 by method of variation of parametersolution to problem on differential questions using variation of parameter method

### orthogonal trajectory of y(1+x ² ) = Cx

find the orthogonal trajectory of y(1+x ² ) = Cxanswer to problem on orthogonal trajectory of y(1+x ² ) = Cx

### orthogonal trajectory of y = (k/x)

find the orthogonal trajectory of y = (k/x)solution to find the orthogonal trajectory of y = (k/x)

formulae on integration

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

### miscellaneous problem from differential equations

miscellaneous problem from differential equations

find the equation of the curve passing through (0,pi/4) whose differential equation is

sinx cosy dx + cosx siny dy =0

here cosy with dx and cosx with dy should be removed.

So divide each term with cosy cosx

the resulting equation is of variable separable type.

integrate term by term

Now to get the value of C, use the given condition that the curve passes through (0,pi/4)

put x =0 and y = pi/4 and solve for C.

is given by x+y+1=A[1-x-y-2xy]

*solve y e^(x/y) = [ y e^(x/y) + (y^2) ]dy [ y is not equal to 0]

solution of differential equation which is not homogeneous but which can be solved using x=vy

solution of a second order differential equation using reduction of order

solve y"-y = 0 if y = coshx is one of the solutions

using the formula for reduction of order

solution of solution of a second order differential equation using reduction of order

solution to problem on differential questions using variation of parameter method

answer to problem on orthogonal trajectory of y(1+x ² ) = Cx

solution to find the orthogonal trajectory of y = (k/x)

formulae on integration

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

find the equation of the curve passing through (0,pi/4) whose differential equation is

sinx cosy dx + cosx siny dy =0

here cosy with dx and cosx with dy should be removed.

So divide each term with cosy cosx

the resulting equation is of variable separable type.

integrate term by term

Now to get the value of C, use the given condition that the curve passes through (0,pi/4)

put x =0 and y = pi/4 and solve for C.

Variable separable differential equation

* show that the general solution of y' + {[ (y^2)+y + 1]/[x^2+x+1] = 0is given by x+y+1=A[1-x-y-2xy]

solution of differential equation which is not homogeneous but which can be solved using x=vy

solve y"-y = 0 if y = coshx is one of the solutions

using the formula for reduction of order

solution of solution of a second order differential equation using reduction of order

### variation of parameter method

solve xy" - 4y' = x^4 by method of variation of parametersolution to problem on differential questions using variation of parameter method

### orthogonal trajectory of y(1+x ² ) = Cx

find the orthogonal trajectory of y(1+x ² ) = Cxanswer to problem on orthogonal trajectory of y(1+x ² ) = Cx

### orthogonal trajectory of y = (k/x)

find the orthogonal trajectory of y = (k/x)solution to find the orthogonal trajectory of y = (k/x)

formulae on integration

PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

PAGE 6 INTEGRATION USING PARTIAL FRACTIONS

disclaimer:

There is no guarantee about the data/information on this site. You use the data/information at your own risk. You use the advertisements displayed on this page at your own risk.We are not responsible for the content of external internet sites. Some of the links may not work

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