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JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

\lim \limits_{\mathrm{n} \rightarrow \infty} \frac{2^{\mathrm{k}}+4^{\mathrm{k}}+6^{\mathrm{k}}+\ldots+(2 \mathrm{n})^{\mathrm{k}}}{\mathrm{n}^{\mathrm{k}+1}}, \mathrm{k} \neq-1

, is equal to

View answer and explanation

Correct option: B

\frac{2^{\mathrm{k}}}{\mathrm{k}+1}

Option B (

\frac{2^{\mathrm{k}}}{\mathrm{k}+1}

) is correct because the limit can be expressed as a Riemann sum and then evaluated as a definite integral.

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[*]

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\int\limits_{{-2}}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x

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I\,\,\left( {m + 1,\,\,n + 1} \right)