For any real number x, let [x] denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by f(x) = x - [x] if [x] is odd, and f(x) = 1 + [x] - x if [x] is even. Then the value of (2/π) ∫-1010 f(x) cos(πx) dx is ________

For any real number x, let [x] denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by f(x) = x - [x] if [x] is odd, and f(x) = 1 + [x] - x if [x] is even. Then the value of (2/π) ∫-1010 f(x) cos(πx) dx is _________.

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Question:

For any real number x, let [x] denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by f(x) = x - [x] if [x] is odd, and f(x) = 1 + [x] - x if [x] is even. Then the value of (2/π) ∫-1010 f(x) cos(πx) dx is _________.

Solution: