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Preview Activity 5.2.1. Consider the function A defined by the rule x A(x) = ™* f(t) dt, where f(t) = 4 – 2t. a. Compute A(1) and A(2) exactly. b. Use the First Fundamental Theorem of Calculus to find a formula for A(x) that does not involve integrals. That is, use the first FTC to evaluate S₁ (4 – 2t) dt. c. Observe that f is a linear function; what kind of function is A?

Preview Activity 5.2.1. Consider the function A defined by the rule x A(x) = ™* f(t) dt, where f(t) = 4 – 2t. a. Compute A(1) and A(2) exactly. b. Use the First Fundamental Theorem of Calculus to find a formula for A(x) that does not involve integrals. That is, use the first FTC to evaluate S₁ (4 – 2t) dt. c. Observe that f is a linear function; what kind of function is A?

Advanced Engineering Mathematics
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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Only need help with questions a through c, thank you!

Preview Activity 5.2.1. Consider the function A defined by the rule A(x) = f* f(t) dt, where f(t) = 4 - 2t. a. Compute A(1) and A(2) exactly. b. Use the First Fundamental Theorem of Calculus to find a formula for A(™) that does not involve integrals. That is, use the first FTC to evaluate S₁ (4 – 2t) dt. c. Observe that f is a linear function; what kind of function is A? d. Using the formula you found in (b) that does not involve integrals, compute A'(x). e. While we have defined f by the rule f(t) = 4 — 2t, it is equivalent to say that f is given by the rule f(x) = 4 - 2x. What do you observe about the relationship between A and f?
Transcribed Image Text:Preview Activity 5.2.1. Consider the function A defined by the rule A(x) = f* f(t) dt, where f(t) = 4 - 2t. a. Compute A(1) and A(2) exactly. b. Use the First Fundamental Theorem of Calculus to find a formula for A(™) that does not involve integrals. That is, use the first FTC to evaluate S₁ (4 – 2t) dt. c. Observe that f is a linear function; what kind of function is A? d. Using the formula you found in (b) that does not involve integrals, compute A'(x). e. While we have defined f by the rule f(t) = 4 — 2t, it is equivalent to say that f is given by the rule f(x) = 4 - 2x. What do you observe about the relationship between A and f?
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