f(t)=4t+1 A(x) = (*₁ f(t) dt B(x) = ( ₁² f(t) dt (4) Let C'(x) = 2x² + x. Write C(r) as an integral of f(t) similar to that of A(x) and B(x). (5) Explain, using geometry and area, why if F(t) is any antiderivative of f(t), then the area beneath f(t) on the interval [1, 8] is given by F(8) - F(1).
f(t)=4t+1 A(x) = (*₁ f(t) dt B(x) = ( ₁² f(t) dt (4) Let C'(x) = 2x² + x. Write C(r) as an integral of f(t) similar to that of A(x) and B(x). (5) Explain, using geometry and area, why if F(t) is any antiderivative of f(t), then the area beneath f(t) on the interval [1, 8] is given by F(8) - F(1).
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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![f(t)=4t+1
A(x) = (* f(t) dt
8(x) = (₁ f(t) dt
(4) Let C'(x) = 2x² + x. Write C(x) as an integral of f(t) similar to that of A(x) and
B(x).
(5) Explain, using geometry and area, why if F(t) is any antiderivative of f(t), then
the area beneath f(t) on the interval [1,8] is given by F(8) - F(1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e9b89df-c7d2-4fa7-b4a5-32520659af16%2F7bf1a412-b6c8-4906-803b-b5b8bea7467f%2Fekv6lki_processed.jpeg&w=3840&q=75)
Transcribed Image Text:f(t)=4t+1
A(x) = (* f(t) dt
8(x) = (₁ f(t) dt
(4) Let C'(x) = 2x² + x. Write C(x) as an integral of f(t) similar to that of A(x) and
B(x).
(5) Explain, using geometry and area, why if F(t) is any antiderivative of f(t), then
the area beneath f(t) on the interval [1,8] is given by F(8) - F(1).
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