Compute the integral from 0 to π of x + sin x

by RoRi

August 3, 2015

Compute

$\int_0^{\pi} (x + \sin x) \, dx.$

We compute the integral as follows:

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

Stumbling Robot

Compute the integral from 0 to π of x + sin x

Related

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment): Cancel reply