If for every integer $n$, $\mathop \smallint \nolimits_n^{n + 1} \,\,f\left( x \right)\,\,dx = {n^2}$,then the value of$\mathop \smallint \nolimits_{ - 2}^4 \,\,f\left( x \right)\,\,dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

If for every integer

n

\int \nolimits_n^{n + 1} \,\,f\left( x \right)\,\,dx = {n^2}

,then the value of

\int \nolimits_{ - 2}^4 \,\,f\left( x \right)\,\,dx

View answer and explanation

Correct option: C

\mathrm{19}

Option C (

\mathrm{19}

) is correct. The integral is evaluated by summing the integrals over the intervals [n, n+1] from -2 to 3.

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