Compute the integral from 0 to (1/2)π^2 of (x^2+ cos x)

by RoRi

August 3, 2015

Compute the following integral:

$\int_0^{\frac{\pi}{2}} (x^2 + \cos x) \, dx.$

We compute as follows:

$\begin{align*} \int_0^{\frac{\pi}{2}} (x^2 + \cos x) \, dx &= \int_0^{\frac{pi}{2}} x^2 \, dx + \int_0^{\frac{\pi}{2}} \cos x \, dx \\ &= \left. \frac{x^3}{3} \right|_0^{\frac{\pi}{2}} + \sin x \biggr \rvert_0^{\frac{\pi}{2}} \\ &= \frac{\pi^3}{24} + \sin \frac{\pi}{2} \\ &= \frac{\pi^3}{24} + 1. \end{align*}$

Stumbling Robot

Compute the integral from 0 to (1/2)π^2 of (x^2+ cos x)

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