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Definite Integration question

2024 · 5 Apr · Shift 2 · Q57

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JEE Main
Mathematics
Definite Integration
2024 · 5 Apr · Shift 2 · Q57

Definite Integration question

2024 · 5 Apr · Shift 2 · Q57

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

If

f(t)=\int\limits_0^\pi \frac{2 x \mathrm{~d} x}{1-\cos^2 \mathrm{t} \sin^2 x}, 0\lt \mathrm{t}\lt \pi

, then the value of

\int\limits_0^{\frac{\pi}{2}} \frac{\pi^2 \mathrm{dt}}{f(\mathrm{t})}

equals

\underline{\hspace{2cm}}

.

Numerical answer

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