Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 5 - Applications Of The Definite Integral In Geometry, Science, And Engineering - 5.1 Area Between Two Curves - Exercises Set 5.1 - Page 353: 3

Answer

$$1$$

Work Step by Step

Determine interval over which to integrate We'll be integrating with respect to $y$ over the interval $1 \leq y \leq \leq 2$ $$ \text{Note that we're merging with y thus it's the right curve minus the left curve.}\\ \begin{array}{c} \int_{1}^{2} y-\frac{1}{y^{2}} d y \\ {\left[\frac{y^{2}}{2}+\frac{1}{y}\right]_{1}^{2}} \\ {\left[\frac{2^{2}}{2}+\frac{1}{2}\right]-\left[\frac{1^{2}}{2}+\frac{1}{1}\right]} \\ {\left[\frac{4}{2}+\frac{1}{2}\right]-\left[\frac{1}{2}+\frac{2}{2}\right]} \\ \frac{5}{2}-\frac{3}{2}=\frac{2}{2}=1 \end{array} $$
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