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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{{\cos x - \sin x}}{{1 + \sin 2x}}\;dx = } $
  • ✓
    $ - \frac{1}{{\cos x + \sin x}} + c$
  • B
    $\frac{1}{{\cos x + \sin x}} + c$
  • C
    $\frac{1}{{\cos x - \sin x}} + c$
  • D
    None of these
✓

Answer

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

required integral is  $ - \frac{1}{{\sin x + \cos x}} + c$.

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