Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.2 - The Definite Integral - 5.2 Exercises - Page 390: 39

Answer

$\frac{25}{4}$

Work Step by Step

On the interval $-4 \leq x \leq 3$, the graph of $\vert \frac{1}{2}x \vert$ forms two triangles above the x-axis. We can find the area of these two triangles: $A = \frac{1}{2}(4)(2)+\frac{1}{2}(3)(\frac{3}{2})$ $A = 4+\frac{9}{4}$ $A = \frac{25}{4}$ Therefore: $\int_{-4}^{3} \vert \frac{1}{2}x \vert~dx = \frac{25}{4}$
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