The value of the definite integral _0^1 e^ e^x (1 + x , , e^x )dx… - Vidyadip

MCQ

The value of the definite integral $\int\limits_0^1 {{e^{{e^x}}}(1 + x\,\cdot\,{e^x})dx} $ is equal to

✓
$e^e$
B
$e^e - e$
C
$e^e - 1$
D
$e$

✓

Answer

Correct option: A.

$e^e$

a
start with $e^x = t$ and use $\int {{e^x}\left( {f(x) + f'(x)} \right)\,dx} $ $= e^x f (x)$

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