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Definite Integration question

2025 · 29 Jan · Shift 2 · Q49

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PYQ Library
JEE Main
Mathematics
Definite Integration
2025 · 29 Jan · Shift 2 · Q49

Definite Integration question

2025 · 29 Jan · Shift 2 · Q49

JEE MainMathematicsDefinite IntegrationNumerical+4 / −1

If

\lim\limits _{t \rightarrow 0}\left(\int\limits_0^1(3 x+5)^t d x\right)^{\frac{1}{t}}=\frac{\alpha}{5 e}\left(\frac{8}{5}\right)^{\frac{2}{3}}

, then

\alpha

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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