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: 11

Answer

$-\frac{3}{2}cos(\frac{2\theta}{3}) +C$

Work Step by Step

Evaluate the Integral using substitution: $\int sin(\frac{2\theta}{3}) d\theta$ Substitution Rule: $\int f(g(x))gā€™(x)dx = \int f(u)du$ $u= \frac{2\theta}{3}$ $du =\frac23$ In this expression du is multipled by $\frac32$ to equal $1$ Solve the integral in terms of $u$: $\int sin(u)(\frac32)du$ $\frac{3}{2}\int sin(u)du $ $-\frac{3}{2}cos(u) +C$ Substitute for $u$: $-\frac{3}{2}cos(\frac{2\theta}{3}) +C$
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