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 336: 7



Work Step by Step

$$A=\int(5+\frac{2}{3}x^2+\frac{3}{4}x^3)dx$$ From Table 1, $$\int cf(x)dx=c\int f(x)dx$$ $$\int[f(x)+g(x)]dx=\int f(x)dx+\int g(x)dx$$ Therefore, $$A=\int5dx+\frac{2}{3}\int(x^2)dx+\frac{3}{4}\int(x^3)dx$$ From Table 1, we also get the followings $$\int kdx=kx+C$$ $$\int (x^n)dx=\frac{x^{n+1}}{n+1}$$ Therefore, $$A=5x+\frac{2}{3}\frac{x^3}{3}+\frac{3}{4}\frac{x^4}{4}+C$$ $$A=5x+\frac{2x^3}{9}+\frac{3x^4}{16}+C$$
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