MCQ
$\int_0^{\pi /2} {\,\,\log \tan x\,dx = } $
- A$\frac{\pi }{2}{\log _e}2$
- B$ - \frac{\pi }{2}{\log _e}2$
- C$\pi {\log _e}2$
- ✓$0$
$ = \int_0^{\pi /2} {\log \sin x\,dx - \int_0^{\pi /2} {\log \cos x\,dx = 0} } $,
$\left\{ \because \int_{0}^{a}{f(x)dx=\int_{0}^{a}{f(a-x)dx}} \right\}$.
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$f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\pi x}{2}\right), & \text { if } x<-1 \\ \left|a x^{2}+x+b\right|, & \text { if }-1 \leq x \leq 1 \\ \sin (\pi x), & \text { if } x>1\end{array}\right.$
વડે વ્યાખ્યાયીત છે. જો $f(x)$ એ $R$ પર સતત હોય, તો $a+b $ ..... .