MCQ
$\int_0^{\pi /2} {\frac{{\cos x}}{{(1 + \sin x)(2 + \sin x)}}} \,dx = $
- ✓$\log \frac{4}{3}$
- B$\log \frac{1}{3}$
- C$\log \frac{3}{4}$
- Dએકપણ નહીં.
so that reduced integral is
$\int_0^1 {\left( {\frac{1}{{1 + t}} - \frac{1}{{2 + t}}} \right)\,\,dt = [\log (1 + t) - \log (2 + t)]_0^1} $
$ = \log \frac{2}{3} - \log \frac{1}{2} = \log \frac{4}{3}$.
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