MCQ
$\int_0^1 {{{\tan }^{ - 1}}x\,dx = } $
- ✓$\frac{\pi }{4} - \frac{1}{2}\log 2$
- B$\pi - \frac{1}{2}\log 2$
- C$\frac{\pi }{4} - \log 2$
- D$\pi - \log 2$
$\Rightarrow dx = {\sec ^2}\theta \,\,d\theta $
Also as $x = 0,\theta = 0$ and $x = 1,\theta = \frac{\pi }{4}$
Therefore, $\int_0^1 {{{\tan }^{ - 1}}x\,dx = \int_0^{\pi /4} {\theta {{\sec }^2}\theta \,d\theta } } $
$ = \frac{\pi }{4}$$ - \log \sqrt 2 = \frac{\pi }{4} - \frac{1}{2}\log 2$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.