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Definite Integration question

2024 · 30 Jan · Shift 1 · Q40

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PYQ Library
JEE Main
Mathematics
Definite Integration
2024 · 30 Jan · Shift 1 · Q40

Definite Integration question

2024 · 30 Jan · Shift 1 · Q40

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

f:\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \rightarrow \mathbf{R}

be a differentiable function such that

f(0)=\frac{1}{2}

. If the

\lim_{x \rightarrow 0} \frac{x \int_0^x f(\mathrm{t}) \mathrm{dt}}{\mathrm{e}^{x^2}-1}=\alpha

, then

8 \alpha^2

is equal to :

A
4
B
2
C
1
D
16

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