Evaluate the following integral: ∫ x sin x cos^2 x dx, x ∈ [0, π]

Question

Evaluate the following integral:

\(\int\limits_{0}^{\pi} \) x sin x cos² x dx

Answer 1

Let us assume

I = \(\int\limits_{0}^{\pi} \) x sin x cos² x dx...equation 1

By property, we know that

Thus

Substituting the given values

We know

b and a being the upper and lower limits respectively