Calculus 8th Edition

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

Chapter 7 - Techniques of Integration - 7.2 Trigonometric Integrals - 7.2 Exercises - Page 524: 11



Work Step by Step

$$\int_{0}^{\frac{\pi}{2}}sin^{2}x\,cos^{2}x\,dx=\int_{0}^{\frac{\pi}{2}}(sin\,x\,cos\,x)^{2}dx$$ $$=\int_{0}^{\frac{\pi}{2}}(\frac{sin2x}{2})^{2}dx$$ $$=\int_{0}^{\frac{\pi}{2}}\frac{1-cos4x}{8}dx$$ $$=\left |\frac{x}{8}-\frac{sin4x}{32} \right |_{0}^{\frac{\pi}{2}}$$ $$=\frac{\pi}{16}$$
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