Calculus, 10th Edition (Anton)

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

Chapter 4 - Integration - 4.9 Evaluating Definite Integrals By Substitution - Exercises Set 4.9 - Page 340: 20

Answer

$$A = \frac{1}{4}$$

Work Step by Step

$$\eqalign{ & {\text{The area is given by}} \cr & A = \int_0^1 {\frac{1}{{{{\left( {3x + 1} \right)}^2}}}} dx \cr & {\text{Integrate and evaluate}} \cr & A = \frac{1}{3}\left[ { - \frac{1}{{3x + 1}}} \right]_0^1 \cr & A = - \frac{1}{3}\left[ {\frac{1}{{3\left( 1 \right) + 1}} - \frac{1}{{3\left( 0 \right) + 1}}} \right] \cr & {\text{Simplify}} \cr & A = - \frac{1}{3}\left( {\frac{1}{4} - 1} \right) \cr & A = \frac{1}{4} \cr} $$
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