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

Question

Evaluate the following Integrals:

\(\int\limits_0^{\pi/2} \)x²sin x dx

Answer 1

Let I =  \(\int\limits_0^{\pi/2} \)x²sin x dx

We will use integration by parts.

Recall,

Here, take f(x) = x² and g(x) = sin x

⇒ f'(x) = 2x

Substituting these values, we evaluate the integral.

We use integration by parts again.

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

⇒ f'(x) = 1

Using these values in equation for I₁