Compute the integral

by RoRi

August 22, 2015

Compute the following integral:

$\int_0^x (u^2 + \sin 3u) \, du.$

We have

$\begin{align*} \int_0^x (u^2 + \sin 3u) \, du &= \int_0^x u^2 \, du + \frac{1}{3} \int_0^{3x} \sin u \, du \\ &= \frac{x^3}{3} + \left. \frac{1}{3}(-\cos u)\right|_0^{3x} \\ &= \frac{x^3}{3} + \frac{1}{3} - \frac{1}{3} \cos 3x. \end{align*}$

Stumbling Robot

Compute the integral

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