If $\left[ {\, \cdot \,} \right]$ denotes the greatest integer function and $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {3\left[ x \right]\,\, - \,\,\frac{{5\,\,\left| {\,x\,} \right|}}{x},\,\,\;x \ne 0}\\ {2\;\;\;\;\;\;\;\;\;\;\;\;\;\;,\,\,x = 0} \end{array}} \right.$ then $\mathop \smallint \limits_{ - 3/2}^2 \,\,f\left( x \right)dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

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

denotes the greatest integer function and

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {3\left[ x \right]\,\, - \,\,\frac{{5\,\,\left| {\,x\,} \right|}}{x},\,\,\;x \ne 0}\\ {2\;\;\;\;\;\;\;\;\;\;\;\;\;\;,\,\,x = 0} \end{array}} \right.

then

\int \limits_{ - 3/2}^2 \,\,f\left( x \right)dx

is equal to

View answer and explanation

Correct option: A

- \frac{{11}}{2}

Option A (-11/2) is correct because the definite integral is evaluated by splitting the integral based on the greatest integer function and absolute value.

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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