Explain why or why not Determine whether the
Chapter 5, Problem 1(choose chapter or problem)
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. Assume f and f_ are continuous functions for all real numbers. a. If A1x2 = 1 x a f 1t2 dt and f 1t2 = 2t - 3, then A is a quadratic function. b. Given an area function A1x2 = 1 x a f 1t2 dt and an antiderivative F of f , it follows that A_1x2 = F 1x2. c. 1 b a f _1x2 dx = f 1b2 - f 1a2. d. If f is continuous on 3a, b4 and 1 b a _ f 1x2 _ dx = 0, then f 1x2 = 0 on 3a, b4. e. If the average value of f on 3a, b4 is zero, then f 1x2 = 0 on 3a, b4. f. 1 b a 12f 1x2 - 3g1x22 dx = 21 b a f 1x2 dx + 31 a b g1x2 dx. g. 1f _1g1x22g_1x2 dx = f 1g1x22 + C.
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