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\(\int_0^{\pi / 4} \tan ^2(x) d x=\)
Options:
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2828 Upvotes
Verified Answer
The correct answer is:
\(1-\frac{\pi}{4}\)
\(\begin{aligned}
I & =\int_0^{\pi / 4} \tan ^2 x d x=\int_0^{\pi / 2}\left(\sec ^2 x-1\right) d x \\
& =[\tan x-x]_0^{\pi / 4}=1-\frac{\pi}{4}
\end{aligned}\)
Hence, option (c) is correct.
I & =\int_0^{\pi / 4} \tan ^2 x d x=\int_0^{\pi / 2}\left(\sec ^2 x-1\right) d x \\
& =[\tan x-x]_0^{\pi / 4}=1-\frac{\pi}{4}
\end{aligned}\)
Hence, option (c) is correct.
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