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Definite Integration question

2023 · Shift 2 · Q25

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2023 · Shift 2 · Q25

Definite Integration question

2023 · Shift 2 · Q25

JEE AdvancedMathematicsDefinite IntegrationNumerical+4 / −1

For

x \in \mathbb{R}

, let

\tan ^{-1}(x) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

. Then the minimum value of the function

f: \mathbb{R} \rightarrow \mathbb{R}

defined by

f(x)=\int\limits_0^{x \tan ^{-1} x} \frac{e^{(t-\cos t)}}{1+t^{2023}} d t

is :

Numerical answer

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