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Definite Integration question

2025 · Shift 2 · Q32

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JEE Advanced
Mathematics
Definite Integration
2025 · Shift 2 · Q32

Definite Integration question

2025 · Shift 2 · Q32

JEE AdvancedMathematicsDefinite IntegrationNumerical+4 / −1

If

\alpha=\int\limits_{\frac{1}{2}}^2 \frac{\tan ^{-1} x}{2 x^2-3 x+2} d x

then the value of

\sqrt{7} \tan \left(\frac{2 \alpha \sqrt{7}}{\pi}\right)

is

\underline{\hspace{2cm}}

. (Here, the inverse trigonometric function

\tan ^{-1} x

assumes values in

\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

.)

Numerical answer

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