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: 43

Answer

$6arcsin(\frac {x-5}5)+C$

Work Step by Step

$10x-x^2=25-(5-x)^2$ $\int \frac 6 {\sqrt {10x-x^2}}dx$ $6\int \frac 1 {\sqrt {25-(5-x)^2}}$ $-6\int \frac {-1} {\sqrt {5^2-(5-x)^2}}$ $-6arcsin(\frac {5-x}5)+C$ $6arcsin(\frac {x-5}5)+C$
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