The value of $\mathop \smallint \nolimits_{ - 1}^1 \,\,\left[ {\,x\,} \right[1 + \sin \,\,{\rm{\pi }}x]\;dx$ is $\left[ {\, \cdot \,} \right]$ denotes the greatest integer)

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \nolimits_{ - 1}^1 \,\,\left[ {\,x\,} \right[1 + \sin \,\,\mathrm{\pi }x]\;dx

\left[ {\, \cdot \,} \right]

denotes the greatest integer)

View answer and explanation

Correct option: A

\mathrm{2}

Option A (2) is correct because the integral simplifies to 2 after considering the greatest integer function and the sine function within the given limits.

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[*]

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