Let f(x) = |x - 1|, g(x) = [x] and h(x) = f(x)g(x) where [.] is greatest integer function. What is ∫_{-1}^0 h(x) dx equal to?

Question

Accepted Answer

-3/2. For x in [-1, 0): [x] = -1, |x - 1| = 1 - x (since x - 1 < 0). So h(x) = (1 - x)(-1) = x - 1. ∫_{-1}^0 (x - 1) dx = [x²/2 - x]_{-1}^0 = (0 - 0) - (1/2 + 1) = -3/2.

Let f(x) = |x - 1|, g(x) = [x] and h(x) = f(x)g(x) where [.] is greatest integer function. What is ∫_{-1}^0 h(x) dx equal to?

Explanation

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