The value of the integral _0^ e ^ -2x , ( , 2x + , 2x) , dx = - Vidyadip

MCQ

The value of the integral $\int\limits_0^\infty {} $ $e ^{-2x}\, (\sin\, 2x + \cos\, 2x)\, dx =$

A
$1$
B
$- 2$
✓
$1/2$
D
zero

✓

Answer

Correct option: C.

$1/2$

c
Put $- 2 x = t$ and use $\int \, e^x ( f (x) + f ‘ (x) ) d x = e^x f (x) + c$]

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