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: 38


$\displaystyle \frac{96}{35}≈2.742857$

Work Step by Step

$\displaystyle \int_0^1(1+x^2)^3dx=\int_0^1(1+x^2+x^2+x^4)(1+x^2)dx=\int_0^1(1+2x^2+x^4)(1+x^2)dx$ $\displaystyle \int_0^11+x^2+2x^2+x^2+2x^4+x^6dx=\int_0^11+3x^2+3x^4+x^6dx$ $\displaystyle (x+x^3+\frac{3x^5}{5}+\frac{x^7}{7})|_0^1$ $\displaystyle [1+1^3+\frac{3(1)^{3/5}}{5}+\frac{(1)^{7}}{7}]-[0+0^3+\frac{3(0)^{3/5}}{5}+\frac{(0)^{7}}{7}]$ $\displaystyle 2+\frac{3}{5}+\frac{1}{7}-0$ $\displaystyle 2+\frac{21}{35}+\frac{5}{35}$ $\displaystyle 2+\frac{26}{35}$ $\displaystyle \frac{70}{35}+\frac{26}{35}$ $\displaystyle \frac{96}{35}≈2.742857$
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