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Question: The value of I= \(\int_{0}^{1}{x\left| x–\frac{1}{2} \right|dx}\) is -...

The value of I= ∫01x∣x–12∣dx\int_{0}^{1}{x\left| x–\frac{1}{2} \right|dx} is -

A

1/3

B

1/4

C

1/8

D

None of these

Answer

1/8

Explanation

Solution

∫01/2–[x(x–1/2)]dx\int_{0}^{1/2}{–\lbrack x(x–1/2)\rbrack dx} + ∫1/21x(x–1/2)dx\int_{1/2}^{1}{x(x–1/2)dx}

– [x3/3–x2/4]01/2\lbrack x^{3}/3–x^{2}/4\rbrack_{0}^{1/2} + [x3/3–x2/4]1/21\lbrack x^{3}/3–x^{2}/4\rbrack_{1/2}^{1} = 1/8