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STD 12 - 7.2 definite integral — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 7.2 definite integral1 Mark
MCQ
$\int_0^\infty {{e^{ - 2x}}(\sin 2x + \cos 2x)\,dx = } $
  • A
    $1$
  • B
    $0$
  • ✓
    $\frac{1}{2}$
  • D
    $\infty $
✓

Answer

Correct option: C.
$\frac{1}{2}$
c
(c) $\int_0^\infty {{e^{ - 2x}}(\sin 2x + \cos 2x)dx} $

$ = \left[ { - {e^{ - x}}\frac{{\cos 2x}}{2}} \right]_0^\infty - \int_0^\infty {\left( { - 2{e^{ - 2x}}} \right)\,} \left( {\frac{{ - \cos 2x}}{2}} \right){\rm{ }}dx$
$ + \int_0^\infty {{e^{ - 2x}}\cos 2x\,dx} $

$ = \frac{1}{2}$.

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