Problem 5. Suppose that F and G are antiderivatives of f and g, respectively. Show that, in general, there is no "product rule" for integrals of the type [ f(x)g(x) dx ‡ F(x)G(x) + C using a counter example. That is, pick (simple!) f and g and show that the inequality above holds.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 36E
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Problem 5.
Suppose that F and G are antiderivatives of ƒ and g, respectively. Show
that, in general, there is no “product rule” for integrals of the type
[ f(x)g(x) da ‡ F(x)G(x) + C
using a counter example. That is, pick (simple!) f and g and show that the inequality above holds.
Transcribed Image Text:Problem 5. Suppose that F and G are antiderivatives of ƒ and g, respectively. Show that, in general, there is no “product rule” for integrals of the type [ f(x)g(x) da ‡ F(x)G(x) + C using a counter example. That is, pick (simple!) f and g and show that the inequality above holds.
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