volume using integral calculus

volume using integral calculus
Volume of the solid obtained by revolving the shaded region about the x-axis is

solved problems on finding volume of solid of revolution using integration

volume of the solid obtained by revolving the ellipse ( x² / a²) + ( y² / b²) = 1 about the x axis


volume of the solid obtained by revolving the cardioid r = a(1 + cosθ ) about the initial line

volume of the spindle shaped solid obtained by revolving the
hypocycloid x^(2/3) + y^(2/3) =a^(2/3) about the x axis.

calculating area using integration

calculation of area using integration (calculus method)
The area of the region bounded by y = f(x) , the x-axis , the horizontal lines x = a , x = b is given by

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The area of the region bounded by x = g(y) , the y-axis , the vertical lines y = c , y = d is given by
some problems on finding area using integration

area under one arch of the cycloid x = a(t-sint) , y =a(1-cost) ----------problem on area by integration

area between y²= x and x²=y -------------area between y²= x and x²=y

find the area of the region {(x,y) / x ² +y ² <= 1 <= x+y}
answer: (pi/4) - (1/2) more explanation on this area question

area bounded by y = x ² +2 and y = 3x ----------area between two curves
area of the cardioid r = a(1 - cosθ ) in polar form ----------- area in polar form

integral of (secx)^4

integral of (secx)^4

split into( sec²x )( sec²x )

change one of the factors into 1+ tan²x
split into two integrals
one is a direct formula integration formulae

for the other integral use substitution method
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