AP EAMCET · Maths · Area Under Curves
The area (in square units) bounded by \(y=\tan ^{-1} x, y=\cot ^{-1} x\) and the \(Y\)-axis, is
- A \(\log _e 4\)
- B \(\log _e 2\)
- C \(\log _e 3\)
- D \(\log _e 5\)
Answer & Solution
Correct Answer
(B) \(\log _e 2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { The required area }=2\left[\frac{\pi}{4}-\int_0^1 \tan ^{-1} x d x\right] \\ & \quad=\frac{\pi}{2}-2 \int_0^1 \tan ^{-1} x d x \\ & \left.\quad=\frac{\pi}{2}-2\left[x \tan ^{-1} x\right)_0^1-\int_0^1 \frac{x}{1+x^2} d x\right] \\ &…
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