mixture: cbse integration guide

Monday, January 16, 2017

integral of 1 / [5 + 4 cosx] with limits 0 to (pi/2)

integral of 1 / [5 + 4 cosx] with limits 0 to (pi/2)

if the denominator contains sinx or cosx in the first degree, the method is to use the substitution,
t = tan(x/2) and change dx
you also have to express sin(x) and cos(x) in terms of tan(x/2) , then use completion of squares if necessary to integrate. If there are limits it is better to change the limits

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integral of linear expression in the numerator mixed with a quadratic expression

integral of ∫ { (4x - 7) / (x² + x +1)} dx

here there is a linear expression in the numerator mixed with quadratic expression containing both (x^2) and x terms

try to express the linear expression in terms of the derivative of the quadratic expression and a constant.
then break the numerator into two parts.
one will be of the form [f '(x) / f(x)] , for the second part use completion of squares.