Suppose that g is an integrable periodic function with period T. (a) If 0 a T, show that
Chapter 10, Problem 27(choose chapter or problem)
Suppose that g is an integrable periodic function with period T. (a) If 0 a T, show that T 0 g(x) dx = a+T a g(x) dx. Hint: Show first that a 0 g(x) dx = a+T T g(x) dx. Consider the change of variable s = x T in the second integral. (b) Show that for any value of a, not necessarily in 0 a T, T 0 g(x) dx = a+T a g(x) dx. (c) Show that for any values of a and b, a+T a g(x) dx = b+T b g(x) dx. 28. I
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