Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 4 - Integration - 4.1 Exercises: 1

Answer

Find the integral of the equation on the left (Left side / LS). Then differentiate the equation on the right (Reft side / RS). Ensure integrating the equation on the left is equal to differentiating the equation on the right. $f(x) = \frac{2}{x^{3}}+C$ $f'(x) = -\frac{6}{x^{4}}$

Work Step by Step

1. Left side (integrate) $\int (-\frac{6}{x^{4}})dx$ $\int (-6x^{-4})dx$ $f(x) = \frac{-6x^{(-4)+(1)}}{(-4)+(1)}$ $f(x) =\frac{-6x^{-3}}{-3}$ $f(x) =2x^{-3}$ $f(x) = \frac{2}{x^{3}}+C$ Therefore, $RS = LS$ 2. Right side (derivative) $f(x) = \frac{2}{x^{3}} + C$ $f(x) = 2x^{-3} + C$ $f'(x) = (-3)(2x^{(-3)-(1)}) + 0$ $f'(x) = -6x^{-4}$ $f'(x) = -\frac{6}{x^{4}}$ Therefore, $LS = RS$
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