Calculus 8th Edition

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

Chapter 7 - Techniques of Integration - 7.5 Strategy for Integration - 7.5 Exercises - Page 547: 18



Work Step by Step

Given $$ \int_{1}^{4}\frac{e^{\sqrt{t}}}{\sqrt{t}} dt$$ Let $u=\sqrt{t}\ \ \ \Rightarrow \ \ \ \dfrac{1}{2\sqrt{t}}dt$, at $x=1\to u=1$ at $x=4\to u=2$then \begin{align*} \int_{1}^{4}\frac{e^{\sqrt{t}}}{\sqrt{t}} dt&=2 \int_{1}^{2} e^{u} du\\ &=2e^u\bigg|_{1}^{2}\\ &=2[e^2-e] \end{align*}
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