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Definite Integration question

2022 · 28 Jul · Shift 1 · Q37

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PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 28 Jul · Shift 1 · Q37

Definite Integration question

2022 · 28 Jul · Shift 1 · Q37

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

The minimum value of the twice differentiable function

f(x)=\int\limits_{0}^{x} \mathrm{e}^{x-\mathrm{t}} f^{\prime}(\mathrm{t}) \mathrm{dt}-\left(x^{2}-x+1\right) \mathrm{e}^{x}

,

x \in \mathbf{R}

, is :

A
$-\frac{2}{\sqrt{\mathrm{e}}}$
B
$-2 \sqrt{\mathrm{e}}$
C
$-\sqrt{\mathrm{e}}$
D
$\frac{2}{\sqrt{\mathrm{e}}}$

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