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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_0^{2\pi } {\frac{{\sin 2\theta }}{{a - b\,\cos \theta }}\,d\theta = } $
  • A
    $1$
  • B
    $2$
  • C
    $\frac{\pi }{4}$
  • ✓
    $0$
✓

Answer

Correct option: D.
$0$
d
(d) $I = \int_0^{2\pi } {\frac{{\sin 2\theta }}{{a - b\cos \theta }}d\theta = \int_0^{2\pi } {\frac{{\sin (2\pi - 2\theta )}}{{a - b\cos (2\pi - \theta )}}d\theta } } $

==> I $ = - \int_0^{2\pi } {\frac{{\sin 2\theta }}{{a - b\cos \theta }}d\theta } $

$ \Rightarrow \,\,2I = 0 $

$\Rightarrow \,\,\int_0^{2\pi } {\frac{{\sin 2\theta }}{{a - b\cos \theta }}d\theta = 0} $..

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