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: 1

Answer

$$\int\cos2xdx=\frac{1}{2}\sin2x$$

Work Step by Step

To evaluate the integral $\int \cos2xdx$ we will use substitution $u=2x$ which gives us $du=2dx\Rightarrow \frac{1}{2}du=dx.$ Putting this into the integral we get: $$\int\cos2xdx=\int\cos u\cdot \frac{1}{2}du=\frac{1}{2}\int\cos udu=\frac{1}{2}\sin u$$ Now we have to express solution in terms of $x$ by expressing $u$ in terms of $x$: $$\int \cos2xdx=\frac{1}{2}\sin u=\frac{1}{2}\sin2x$$
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