Let ∫_α^(log e 4) (d x)/(√(eˣ-1))=(π)/6. Then e^α and e^(-α) are the roots of the equation:

Integral Calculus: JEE Main 2024 Mathematics question

JEE Main 2024 · 8 Apr, Evening shift · Q3483

JEE Main 20248 Apr, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

Let

\int_\limits\alpha^{\log _e 4} \frac{\mathrm{d} x}{\sqrt{\mathrm{e}^x-1}}=\frac{\pi}{6}

. Then

\mathrm{e}^\alpha

and

\mathrm{e}^{-\alpha}

are the roots of the equation :

JEE Main 2024 · 8 Apr, Evening shift · Q3483

JEE Main 20248 Apr, Evening shiftMathematicsMediumIntegral Calculus369× since 2002

Let

\int_\limits\alpha^{\log _e 4} \frac{\mathrm{d} x}{\sqrt{\mathrm{e}^x-1}}=\frac{\pi}{6}

. Then

\mathrm{e}^\alpha

and

\mathrm{e}^{-\alpha}

are the roots of the equation :