$\mathop \smallint \nolimits_{ - 2}^{10} \,{\rm{sgn}}\,(x - \,\,\left[ x \right]\,dx$ Equals, where $\left[ {\,{\rm{.}}\,} \right]\,$ denotes greatest integer function

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \nolimits_{ - 2}^{10} \,\mathrm{sgn}\,(x - \,\,\left[ x \right]\,dx

Equals, where

\left[ {\,\mathrm{.}\,} \right]\,

denotes greatest integer function

View answer and explanation

Correct option: C

\mathrm{8}

Option C (8) is correct because the integral of the sign function simplifies to the difference between the lengths of the positive and negative intervals.

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