1. Let f: [a, b] → R be a strictly increasing function, which is continuous on [a, b] and differentiable on (a, b). (a) Show that X f(x) -1 Så ƒ(t) dt + [{²ð ƒ¯¹(1) dl = rf(x) — aƒ(a), ¥x€([a,b]. a f(a) Give a geometric interpretation of this equality. 2 2 (b) Compute √ √t dt and f² ln(t) dt using the result obtained in the previous part.
1. Let f: [a, b] → R be a strictly increasing function, which is continuous on [a, b] and differentiable on (a, b). (a) Show that X f(x) -1 Så ƒ(t) dt + [{²ð ƒ¯¹(1) dl = rf(x) — aƒ(a), ¥x€([a,b]. a f(a) Give a geometric interpretation of this equality. 2 2 (b) Compute √ √t dt and f² ln(t) dt using the result obtained in the previous part.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...
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