Answer:
Option B
Explanation:
Let l=$\int_{0}^{\pi/4} x.\sec^{2}x dx$
$\Rightarrow$ $l=[x\int \sec^{2}x dx]^{\pi/4}_{0}-\int_{0}^{\pi/4} \left(\frac{dy}{dx}\int \sec^{2}x dx\right) dx$
[integration by parts]
$\Rightarrow$ $l=[x\tan^{}x ]^{\pi/4}_{0}-\int_{0}^{\pi/4} \tan x dx$
$\Rightarrow$ $l=[\frac{\pi}{4}\tan^{}\frac{\pi}{4}-0 ]-[\log \sec x]^{\pi/4}_{0}$
$\Rightarrow$ $l=\frac{\pi}{4}-\left( \log \sec\frac{\pi}{4}-\log \sec 0\right)$
$l=\frac{\pi}{4}-\left( \log\sqrt{2}-\log 1\right)$
$\Rightarrow$ l= $\frac{\pi}{4}-\log \sqrt{2}$
