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NTA Abhyas JEE Main2020MathematicsInverse Trigonometric FunctionsPractice

The area bounded by the curve y = c o s - 1 sin ⁡ x + π 2 - c o s - 1 cos ⁡ x and the x -axis, where π 2 ≤ x ≤ π , is equal to

Options

  1. Aπ 2
  2. Bπ 2 2
  3. Cπ 2 8
  4. Dπ 2 4

Correct answer

D. π 2 4

Step-by-step solution

y = π 2 - s i n - 1 sin ⁡ x + π 2 - c o s - 1 cos ⁡ x For x ∈ π 2 , π y = π 2 - π - x + π 2 - x y = x - π 2 + π 2 - x y = x - π 2 + x - π 2 = 2 x - π Area = 1 2 × π 2 × π = π 2 4

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