X A(x) = √²³ ƒ 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? 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?

X A(x) = √²³ ƒ 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? 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?

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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