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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{x^2}\sin 2x} \;dx = $
  • A
    $\frac{1}{2}{x^2}\cos 2x + \frac{1}{2}x\sin 2x + \frac{1}{4}\cos 2x + c$
  • ✓
    $ - \frac{1}{2}{x^2}\cos 2x + \frac{1}{2}x\sin 2x + \frac{1}{4}\cos 2x + c$
  • C
    $\frac{1}{2}{x^2}\cos 2x - \frac{1}{2}x\sin 2x + \frac{1}{4}\cos 2x + c$
  • D
    None of these
✓

Answer

Correct option: B.
$ - \frac{1}{2}{x^2}\cos 2x + \frac{1}{2}x\sin 2x + \frac{1}{4}\cos 2x + c$
b
(b) Let $I = \int_{}^{} {{x^2}\sin 2x\,dx} = \frac{{ - {x^2}\cos 2x}}{2} + \int_{}^{} {\frac{{2x\cos 2x}}{2}\,dx} + c$
$ = - \frac{{{x^2}\cos 2x}}{2} + \frac{{x\sin 2x}}{2} + \frac{{\cos 2x}}{4} + c.$

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