Question

${\int }_0^{\frac{\pi }{2}}logtanxdx=$ [MP PET 1999; RPET 2001, 02; Karnataka CET 1999, 2000, 01, 02]

• A.
  
• B.
  
• C.
  
• D. $0$

Answer 1

The correct option is D $0$

${\int }_0^{\frac{\pi }{2}}logtanxdx={\int }_0^{\frac{\pi }{2}}log\left(\frac{sinx}{cosx}\right)dx$
$={\int }_0^{\frac{\pi }{2}}logsinxdx-{\int }_0^{\frac{\pi }{2}}logcosxdx=0,$
$\{\because {\int }_0^{a}f\left(x\right)dx={\int }_0^{a}f(a-x)dx\}$