Evaluate the following Integrals:

Let

We will use integration by parts.

Recall,

Here, take f(x) = x² and g(x) = sin x

Now,

⇒ f’(x) = 2x

Substituting these values, we evaluate the integral.

Let

We use integration by parts again.

Here, take f(x) = x and g(x) = cos x

Now,

⇒ f’(x) = 1

Using these values in equation for I₁

Substituting I₁ in I, we get

⇒ I = (0 + π + 0) – (2)

⇒ I = π – 2