The value of $I = \mathop \smallint \nolimits_0^1 \,\,x\,\,\left| {\,x\,\, - \,\,\frac{1}{2}\,} \right|\,\,dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

I = \int \nolimits_0^1 \,\,x\,\,\left| {\,x\,\, - \,\,\frac{1}{2}\,} \right|\,\,dx

View answer and explanation

Correct option: C

\mathrm{1}\,\mathrm{/}\,\mathrm{8}

Option C (

\mathrm{1}\,\mathrm{/}\,\mathrm{8}

) is correct because the definite integral is evaluated by splitting the integral at x=1/2 due to the absolute value function.

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I\,\,\left( {m,\,\,n} \right) = \int \nolimits_0^1 \,\,{t^m}\,\,{\left( {1 + t} \right)^n}\,\,dt

I\left( {m,\,\,n} \right)

I\,\,\left( {m + 1,\,\,n + 1} \right)