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 - Page 253: 74

Answer

False

Work Step by Step

For example, let f(x) = g(x) = x Therefore, LHS = $ \int x . x dx =\int x^2 dx = \frac{x^3}{3} $ whereas RHS = $ \int x dx \int x dx = \frac{x^2}{2}\frac{x^2}{2} = \frac{x^4}{4}$ Clearly, LHS$\ne$RHS and hence the given statement is proven false by counter-example
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