Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises: 64

Answer

$\int_0^7\frac{1}{\sqrt {100-x^{2}}}dx=arcsin\frac{7}{10}$

Work Step by Step

$\int_0^7\frac{1}{\sqrt {100-x^{2}}}dx$ $=\int_0^7\frac{1}{\sqrt {(10)^{2}-x^{2}}}dx$ Use arcsine formula: $arcsin\frac{u}{a}+C=\int \frac{1}{\sqrt {a^{2}-u^{2}}}du$ $=arcsin\frac{x}{10}|_0^7$ $=arcsin\frac{7}{10}-arcsin0$ $=arcsin\frac{7}{10}-0$ $=arcsin\frac{7}{10}$
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