Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 6 - Section 6.1 - Areas Between Curves - 6.1 Exercises - Page 434: 22

Answer

$$A = \frac{1}{2} $$
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Work Step by Step

From the graph, we can see that $x \geq x^{3}$ on the interval $[0,1]$; therefore, the area between the two curves is $$A=2\displaystyle\int_{0}^{1} x-x^{3} \space dx$$ $$A = 2 \bigg[\frac{x^{2}}{2} - \frac{x^{4}}{4} \bigg]^{1}_0$$ $$A=2\bigg[\frac{1}{2}-\frac{1}{4}\bigg]=\frac{1}{2}$$
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