Evaluate the following Integrals:

Given Definite Integral can be written as:

Let us write numerator in terms of the denominator for easy calculation,

⇒ sinx = K(sinx+cosx) + L(cosx – sinx)

⇒ sinx = sinx(K-L) +cosx(K+L)

Comparing coefficients of corresponding terms on both sides we get,

⇒ K + L =0

⇒ K – L =1

On solving these two equations we get,

L= and K = .

So numerator can be written as:

Substituting these values in(1) we get,

We know that:

We know that:

[here f’(x) is derivative of f(x)).