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7.1 inderfinite integral — Maths STD 12 Science — Question

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

Answer

Correct option: B.
$\frac{1}{{b(a + b\cos x)}} + c$
b
(b) Put $a + b\cos x = t \Rightarrow dx = - \frac{{dt}}{{b\sin x}},$ then
$\int_{}^{} {\frac{{\sin x}}{{{{(a + b\cos x)}^2}}}\,dx = - \frac{1}{b}\int_{}^{} {\frac{1}{{{t^2}}}\,dt} = \frac{1}{b}\frac{1}{t} + c} $
$ = \frac{1}{{b(a + b\cos x)}} + c.$

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