The value of ∫01 x3(1−x)11dx is equal to

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111+312+313+114

−111+312−313+114

813

111−312+314−114

answer is D.

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Detailed Solution

Given integral is equal to ∫01 (1−x)3(1−(1−x))11dx=∫01 x11(1−x)3dx=∫01 x111−3x+3x2−x3dx=∫01 x11−3x12+3x13−x14dx=111−312+313−114