Calculus 8th Edition

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

Chapter 4 - Integrals - 4.5 The Substitution Rule - 4.5 Exercises: 17

Answer

$\frac{tan^4\theta}{4} +C$

Work Step by Step

Evaluate the Integral using substitution: $\int sec^2(\theta )tan^3(\theta) d\theta$ Substitution Rule: $\int f(g(x))gā€™(x)dx = \int f(u)du$ $u= tan(\theta)$ $du =sec^2(\theta)$ Solve the integral in terms of $u$: $\int (u)^3du$ $\frac{u^4}{4}+C $ Substitute for $u$: $\frac{tan^4\theta}{4} +C$
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