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f:[0,1)toR be a non increasing function the for alpha epsilon(0,1) |
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Answer» `alpha int_(0)^(1)f(x) DX le int_(0)^(alpha)f(x)dx` Put `x=alphat` `:. int_(0)^(alpha) f(x)dx=alpha int_(0)^(1)f (alpha t)dt ge alpha int_(0)^(1)f(t)dt` as `alpha epsilon(0,1)` ALSO `alpha int_(0)^(1) f(t)dt ge alpha^(2) int_(0)^(1)f(t)dt` `:. int_(0)^(alpha)f(x)dxgealpha^(2)int_(0)^(1)f(x)dx` |
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