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: 16

Answer

$-2cos(\sqrt x) +C$

Work Step by Step

Evaluate the Integral using substitution: $\int \frac{sin\sqrt x}{\sqrt x}$ Substitution Rule: $\int f(g(x))gā€™(x)dx = \int f(u)du$ $u= \sqrt x$ $du =\frac{1}{2\sqrt x}$ Since $du$ in the expression is equal to $\frac{1}{\sqrt x}$ it must be multiplied by $2$ Solve the integral in terms of $u$: $\int sin(u)(2)du$ $-2cos(u) +C $ Substitute for $u$: $-2cos(\sqrt x) +C$
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