Solve $\int_{0}^{x / 4} \tan ^{2} x d x$ - Noon Academy

Solve $\int_{0}^{x / 4} \tan ^{2} x d x$

Maths | Previous Year Question Papers

Solve $\int_{0}^{x / 4} \tan ^{2} x d x$

$\tan ^{2} \mathrm{x}=\sec ^{2} \mathrm{x}-1$
$\Rightarrow \int_{0}^{\pi / 4}-1 \mathrm{dx}+\int_{0}^{\pi / 4}\left(\sec ^{2} \mathrm{x}\right) \mathrm{dx}$
$=-\pi / 4+[\tan \mathrm{x}\}_{0}^{\pi / 4}$
$=1-\pi / 4$

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