If $f\,\,\left( x \right) = \,\,\left\{ {\,\begin{array}{*{20}{c}} {\left| {\,x\,} \right|,}\\ {\left| {x - 2} \right|,} \end{array}\begin{array}{*{20}{c}} { - 1\,\,\, \le \,\,\,x\,\,\, \le 1}\\ {1\,\, < \,\,\,x\,\,\, \le 3} \end{array}} \right.$ then $\mathop \smallint \nolimits_{ - 1}^3 \,\,f\,\,\left( x \right)\,\,dx$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

f\,\,\left( x \right) = \,\,\left\{ {\,\begin{array}{cccccccccccccccccccc} {\left| {\,x\,} \right|,}\\ {\left| {x - 2} \right|,} \end{array}\begin{array}{cccccccccccccccccccc} { - 1\,\,\, \le \,\,\,x\,\,\, \le 1}\\ {1\,\, < \,\,\,x\,\,\, \le 3} \end{array}} \right.

then

\int \nolimits_{ - 1}^3 \,\,f\,\,\left( x \right)\,\,dx

is equal to

View answer and explanation

Correct option: C

\mathrm{2}

Option D (2) is correct because the integral is evaluated by splitting the integral based on the piecewise function definition and then integrating each part.

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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