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The area enclosed by the curve y = cot x, the line x = pi/4, and the x-axis (y = 0) can be represented as:

1. (A) ∫[0 to π/4] tan(π/4 − x) dx
2. (B) π/4 − ∫[0 to 1] tan^−1 x dx
3. (C) 1 − ∫[0 to 1] tan^−1 x dx
4. (D) ∫[0 to π/4] tan^−1 x dx

Correct answer: (B) π/4 − ∫[0 to 1] tan^−1 x dx

Solution

Integrating horizontally, the area = ∫0¹ (pi/2 - arctan y - pi/4) dy = pi/4 - ∫0¹ arctan x dx, matching option (B).

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