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: 12

Answer

$\frac{tan(2\theta)}{2} +C$

Work Step by Step

Evaluate the Integral using substitution: $\int sec^2(2\theta)d\theta$ Substitution Rule: $\int f(g(x))gā€™(x)dx = \int f(u)du$ $u= 2\theta$ $du =2$ Since $du$ in the expression is equal to $1$ it must be multiplied by $\frac{1}{2} $ Solve the integral in terms of $u$: $\int sec^2(u)(\frac12)du$ $\frac{1}{2}\int sec^2(u)du $ $\frac{1}{2}tan(u) +C$ $\frac{tan(u)}{2} + C$ Substitute for $u$: $\frac{tan(2\theta)}{2} +C$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.