Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 4 - Integrals - Review - Exercises - Page 349: 4

Answer

$\int_0^\pi \sin(x) dx=2$

Work Step by Step

$$\begin{align*} \lim_{n \to \infty}\sum_{i=1}^{n}\sin(x_i)\Delta x&=\int_0^\pi \sin(x) dx\\ &=[-\cos(x)]_0^\pi\\ &=-\cos(\pi)-(-\cos(0))\\ &=1+1\\ &=2 \end{align*}$$
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