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

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Evaluate the following Integrals:

$\int\limits_0^{\pi/2}$x2sin x dx

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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