Let g be continuous on [a, b] where g(x) > 0 for all x € [a, b] and define F(t) = f g(x)dx for te [a, b]. Show that if f is continuous, then [far = [ fdF f f(x)g(x)dx.
Let g be continuous on [a, b] where g(x) > 0 for all x € [a, b] and define F(t) = f g(x)dx for te [a, b]. Show that if f is continuous, then [far = [ fdF f f(x)g(x)dx.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 52E
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![5. Let g be continuous on [a, b] where g(x) > 0 for all x = [a, b] and define F(t) = f g(x)dx for
te [a, b]. Show that if f is continuous, then
a
fa
fdF
= [ f
a
f(x)g(x) dx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F655e5d67-ab19-404c-b883-3aa3c693f6a1%2F887f3d5b-3ba8-4b41-927a-488ac8bc0873%2Fdkul32a_processed.png&w=3840&q=75)
Transcribed Image Text:5. Let g be continuous on [a, b] where g(x) > 0 for all x = [a, b] and define F(t) = f g(x)dx for
te [a, b]. Show that if f is continuous, then
a
fa
fdF
= [ f
a
f(x)g(x) dx.
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