_0^ / 4 ^2 x d x is equal to : - Vidyadip

Question

$\int_0^{\pi / 4} \tan ^2 x d x$ is equal to :

✓

Answer

(A)
$
\begin{aligned}
\int_0^{\pi / 4} \tan ^2 x d x & =\int_0^{\pi / 4}\left(\sec ^2 x-1\right) d x \\
& =\int_0^{\pi / 4} \sec ^2 x d x-\int_0^{\pi / 4} d x \\
& =(\tan x)_0^{\frac{\pi}{4}}-(x)_0^{\frac{\pi}{4}} \\
& =\left(\tan \frac{\pi}{4}-\tan 0\right)-\left(\frac{\pi}{4}-0\right) \\
& =\left(\tan \frac{\pi}{4}-0-\frac{\pi}{4}\right)=1-\frac{\pi}{4}
\end{aligned}
$
Hence option (A) is correct.

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