AP EAMCET · Maths · Definite Integration
\(\int_0^{\pi / 4}\left(\tan ^2 x-\tan ^4 x\right) d x=\)
- A 3
- B 2
- C \(\frac{1}{3}\)
- D 0
Answer & Solution
Correct Answer
(C) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \int_0^{\frac{\pi}{4}}\left(\tan ^2 x+\tan ^4 x\right) d x \\ & \int_0^{\frac{\pi}{4}}\left(1+\tan ^2 x\right) \tan ^2 x d x \\ & \int_0^{\frac{\pi}{4}} \sec ^2 x \cdot \tan ^2 x d x \\ & \text {Put, } \tan x=t \\ & \sec ^2 x d x=d t \end{aligned}\) when…
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