Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 337: 29



Work Step by Step

We can rewrite this integral as $\int_1^4 (5x^{-1})^{\frac{1}{2}}dx = \int_1^4 5^{\frac{1}{2}}x^{-\frac{1}{2}}dx $ to see that we can treat $5^{\frac{1}{2}}$ as a constant and move it out of the integrand, making our integral $(5^{\frac{1}{2}})\int_1^4 x^{-\frac{1}{2}}dx $ instead Evaluating the integral gives us $2x^\frac{1}{2}\big|_1^4$ Substituting in $4$ and $1$ gives us $(2 \sqrt 4 ) - (2 \sqrt 1) = 4 - 2 = 2 $ We now multiply our answer by $(5^{\frac{1}{2}})$ and get $2\sqrt5$ as our final answer
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