MCQ
$\int_0^\pi {\frac{{x\tan x}}{{\sec x + \tan x}}} \,dx = $
- A$\frac{\pi }{2} - 1$
- B$\pi \left( {\frac{\pi }{2} + 1} \right)$
- C$\frac{\pi }{2} + 1$
- ✓$\pi \left( {\frac{\pi }{2} - 1} \right)$
==> $2I = \frac{\pi }{2}\int_0^\pi {\frac{{\tan x}}{{\sec x + \tan x}}dx = \frac{\pi }{2}\int_0^\pi {\frac{{\sin x}}{{1 + \sin x}}dx} } $
$=\frac{\pi }{2}\left[ {\int_0^\pi {1dx - \int_0^\pi {\frac{{dx}}{{1 + \sin x}}} } } \right]$
On solving, we get $I = \frac{{{\pi ^2}}}{2} - \pi = \pi \left( {\frac{\pi }{2} - 1} \right)$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.