Explain why or why not Determine whether the

Chapter 5, Problem 53

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Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. If f is a constant function on the interval 3a, b4, then the right and left Riemann sums give the exact value of 1 b a f 1x2 dx, for any positive integer n. b. If f is a linear function on the interval 3a, b4, then a midpoint Riemann sum gives the exact value of 1 b a f 1x2 dx, for any positive integer n. c. 1 2p>a 0 sin ax dx = 1 2p>a 0 cos ax dx = 0. (Hint: Graph the functions and use properties of trigonometric functions.) d. If 1 b a f 1x2 dx = 1 a b f 1x2 dx, then f is a constant function. e. Property 4 of Table 5.4 implies that 1 b a x f 1x2 dx = x1 b a f 1x2 dx.

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