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Definite Integration question

2024 · 30 Jan · Shift 1 · Q32

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PYQ Library
JEE Main
Mathematics
Definite Integration
2024 · 30 Jan · Shift 1 · Q32

Definite Integration question

2024 · 30 Jan · Shift 1 · Q32

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

The value of

\lim_{n \rightarrow \infty} \sum_{k=1}^n \frac{n^3}{\left(n^2+k^2\right)\left(n^2+3 k^2\right)}

is :

A
$\frac{\pi}{8(2 \sqrt{3}+3)}$
B
$\frac{(2 \sqrt{3}+3) \pi}{24}$
C
$\frac{13 \pi}{8(4 \sqrt{3}+3)}$
D
$\frac{13(2 \sqrt{3}-3) \pi}{8}$

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