JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

Let

C_n=\int_{1 / n+1}^{1 / n} \frac{\tan ^{-1}(n x)}{\sin ^{-1}(n x)} d x

, then

\lim _{n \rightarrow \infty} n^2 \cdot C_n

is equal to

View answer and explanation

Correct option: D

\frac{1}{2}

Option D (

\frac{1}{2}

) is correct because the limit is evaluated using L'Hopital's rule and the Leibniz rule for differentiation under the integral sign.

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