Calculus 8th Edition

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

Chapter 4 - Integrals - 4.2 The Definite Integral - 4.2 Exercises - Page 318: 42

Answer

$-\frac{3}{8}\pi$

Work Step by Step

Use the propriety of definite integrals: $$\int_a^b f(x)=-\int_b^a f(x)$$ $$\int_{\pi}^{0}\sin^{4}(\theta)d\theta=\int_{\pi}^{0}\sin^{4}(x)dx=-\int_{0}^{\pi}\sin^{4}(x)dx=-\frac{3}{8}\pi$$
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