Explain why or why not Determine whether the
Chapter 5, Problem 53(choose chapter or problem)
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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