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Definite Integration question

2024 · 9 Apr · Shift 1 · Q52

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JEE Main
Mathematics
Definite Integration
2024 · 9 Apr · Shift 1 · Q52

Definite Integration question

2024 · 9 Apr · Shift 1 · Q52

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

Let

\lim_{n \rightarrow \infty}\left(\frac{n}{\sqrt{n^4+1}}-\frac{2 n}{\left(n^2+1\right) \sqrt{n^4+1}}+\frac{n}{\sqrt{n^4+16}}-\frac{8 n}{\left(n^2+4\right) \sqrt{n^4+16}}\right.\left.+\ldots+\frac{n}{\sqrt{n^4+n^4}}-\frac{2 n \cdot n^2}{\left(n^2+n^2\right) \sqrt{n^4+n^4}}\right)

be

\frac{\pi}{k}

, using only the principal values of the inverse trigonometric functions. Then

\mathrm{k}^2

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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