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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {2\sin x} \cos x\;dx$ is equal to
  • A
    $\cos 2x + c$
  • B
    $\sin 2x + c$
  • C
    ${\cos ^2}x + c$
  • ✓
    ${\sin ^2}x + c$
✓

Answer

Correct option: D.
${\sin ^2}x + c$
d
(d) $I = \int_{}^{} {2\sin x\,.\,\cos x\,dx} = \int_{}^{} {\sin 2x\,dx} $
$ = - \frac{{\cos 2x}}{2} + c = - \frac{{(1 - 2{{\sin }^2}x)}}{2} + c$
$ = - \frac{1}{2} + {\sin ^2}x + c = {\sin ^2}x + c$.

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