The value of integral $\mathop \smallint \nolimits_{ - 1}^1 \,\,\frac{{\left| {\,x\,\, + \,\,2\,} \right|}}{{x\,\, + \,\,2}}\;\,\,dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of integral

\int \nolimits_{ - 1}^1 \,\,\frac{{\left| {\,x\,\, + \,\,2\,} \right|}}{{x\,\, + \,\,2}}\;\,\,dx

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Correct option: B

\mathrm{2}

Option B (2) is correct because since x + 2 is positive over the interval [-1, 1], the absolute value simplifies, and the integral becomes

\int_{-1}^{1} 1 dx = 2

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