If $f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {{e^{\cos x}}\,\,\sin \,\,x,}\\ {2,} \end{array}\,\,\begin{array}{*{20}{c}} {\left| {\,x\,} \right|\,\, \le \,\,2}\\ {{\rm{otherwise}}} \end{array},} \right.$ then $\mathop \smallint \nolimits_{ - 2}^3 \,\,f\left( x \right)\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

f\left( x \right) = \left\{ {\begin{array}{cccccccccccccccccccc} {{e^{\cos x}}\,\,\sin \,\,x,}\\ {2,} \end{array}\,\,\begin{array}{cccccccccccccccccccc} {\left| {\,x\,} \right|\,\, \le \,\,2}\\ {\mathrm{otherwise}} \end{array},} \right.

then

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

is equal to

View answer and explanation

Correct option: C

\mathrm{2}

Option C (2) is correct because the integral can be split into two parts, where the first part is zero due to the odd function and the second part evaluates to 2.

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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