AP EAMCET · Maths · Indefinite Integration
\(\int_0^{\pi / 4} \tan ^2(x) d x=\)
- A \(\frac{\pi}{4}\)
- B \(\frac{\pi}{4}-1\)
- C \(1-\frac{\pi}{4}\)
- D 0
Answer & Solution
Correct Answer
(C) \(1-\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} I & =\int_0^{\pi / 4} \tan ^2 x d x=\int_0^{\pi / 2}\left(\sec ^2 x-1\right) d x \\ & =[\tan x-x]_0^{\pi / 4}=1-\frac{\pi}{4} \end{aligned}\) Hence, option (c) is correct.
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