MCQ
$\int_0^{\pi /2} {\log \,\left( {\frac{{4 + 3\sin x}}{{4 + 3\cos x}}} \right)} \,dx =$
- A$2$
- B$\frac{3}{4}$
- ✓$0$
- Dએકપણ નહીં.
==> $I = \int_0^{\pi /2} {\log \left( {\frac{{4 + 3\cos x}}{{4 + 3\sin x}}} \right)} \,dx$,
$\left[ \because \int_{0}^{\pi /2}{f(x)dx=\int_{0}^{\pi /2}{f\left( \frac{\pi }{2}-x \right)\,dx}} \right]$
==> $I = - \int_0^{\pi /2} {\log \left( {\frac{{4 + 3\sin x}}{{4 + 3\cos x}}} \right)\,dx = - I} $
==> $2I = 0 \Rightarrow I = 0$.
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