The value of${\mathop{\rm l}\nolimits} \mathop {\,\smallint }\nolimits_{ - 2}^0 \,\,\left[ {{x^3} + 3{x^2} + 3x + 3 + \left( {x + 1} \right)\,\,\cos \,\,\left( {x + 1} \right)} \right]\,\,dx$ is

$\begin{array}{*{20}{l}} {\rm{4}} \end{array}$

$\begin{array}{*{20}{l}} {\rm{0}} \end{array}$

$\begin{array}{*{20}{l}} {\rm{3}} \end{array}$

$\begin{array}{*{20}{l}} {\rm{1}} \end{array}$

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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

The value of

{\mathop\mathrm{l}\nolimits} \mathop {\,\int }\nolimits_{ - 2}^0 \,\,\left[ {{x^3} + 3{x^2} + 3x + 3 + \left( {x + 1} \right)\,\,\cos \,\,\left( {x + 1} \right)} \right]\,\,dx

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Correct option: C

\begin{array}{llllllllllllllllllll} \mathrm{4} \end{array}

Option C (4) is correct because the integral simplifies to the integral of an odd function plus a constant, and the integral of the odd function over a symmetric interval is zero.

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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