2. Let I = [a, b] and let ƒ : I → R be continuous on I. Let J = let v : J [c, d] and → R be differentiable on J and satisfy v(J) C I. Show that if G : J → R is defined by G(x) = | f(t)dt, x € J, then G is differentiable , and find G'(x) for x E J.
2. Let I = [a, b] and let ƒ : I → R be continuous on I. Let J = let v : J [c, d] and → R be differentiable on J and satisfy v(J) C I. Show that if G : J → R is defined by G(x) = | f(t)dt, x € J, then G is differentiable , and find G'(x) for x E J.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![[a, b] and let f : I → R be continuous on I. Let J :
let v : J → R be differentiable on J and satisfy v(J) C I. Show that if
[c, d] and
2. Let I
G : J → R is defined by
sv(x)
G(x) = | f(t)dt, æ € J,
a
then G is differentiable , and find G'(x) for x E J.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d456ce1-cbfb-470f-8ef9-05bd7d57f044%2F581b30b4-3dcd-4644-b03b-1d1a412a07e3%2Frhcjyt3d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[a, b] and let f : I → R be continuous on I. Let J :
let v : J → R be differentiable on J and satisfy v(J) C I. Show that if
[c, d] and
2. Let I
G : J → R is defined by
sv(x)
G(x) = | f(t)dt, æ € J,
a
then G is differentiable , and find G'(x) for x E J.
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