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Definite Integration question

2021 · 26 Feb · Shift 2 · Q31

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JEE Main
Mathematics
Definite Integration
2021 · 26 Feb · Shift 2 · Q31

Definite Integration question

2021 · 26 Feb · Shift 2 · Q31

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

f(x) = \int\limits_0^x {{e^t}f(t)dt + {e^x}}

be a differentiable function for all x

\in

R. Then f(x) equals :

A
${e^{({e^{x - 1}})}}$
B
$2{e^{{e^x}}} - 1$
C
$2{e^{{e^x} - 1}} - 1$
D
${e^{{e^x}}} - 1$

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