Calculate the integral of f (x) = max (x ,1-x) for x in [0,1]?
Question: Calculate the integral of f (x) = max (x ,1-x) for x in [0,1]?
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- Calculate ∫ f (x) dx for x € [0,1] ⌠ 1 ⌠ 0.5 ------------- --------------- ⌠ 1 ⌠ 0 f (x) dx = ⌠ 0 (1-x) dx + x dx ⌠ 0.5 because in the interval [0,0.5] ≥ 1-x and x in the interval [0.5,1] x 1-x ≥ ⌠ 0.5 --------------------- 1 ------------- 1 ⌠ 0 f (x) dx = [x-x ² / 2] + [x ² / 2] = (0.5-0.25 / 2) + (1/2-0.25/2) ------------------------ - 0 ---------------- 0.5 = 0.75
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