JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

\operatorname{Lim}_{n \rightarrow \infty}\left(\frac{(n+1)^{1 / 3}}{n^{4 / 3}}+\frac{(n+2)^{1 / 3}}{n^{4 / 3}}+\ldots .+\frac{(2 n)^{1 / 3}}{n^{4 / 3}}\right)

is equal to :

View answer and explanation

Correct option: B

\frac{3}{4}(2)^{4 / 3}-\frac{3}{4}

Option B (

\frac{{3}}{{4}}

(2)^{{4/3}}-

\frac{{3}}{{4}}

) is correct because the limit of the sum can be expressed as a definite integral, which can then be evaluated.

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