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NTA Abhyas JEE Main2020MathematicsArea Under CurvesPractice

The area of the closed region bounded by y = sec - 1 ⁡ x , y = c o s e c - 1 x and the line x - 1 = 0 is

Options

  1. Alog e ⁡ 3 + 2 2 - π 2 s q . u n i t s
  2. Bπ 2 - log e ⁡ 3 + 2 2 s q . u n i t s
  3. Cπ - 3 log e ⁡ 3 s q . u n i t s
  4. DNone of these

Correct answer

A. log e ⁡ 3 + 2 2 - π 2 s q . u n i t s

Step-by-step solution

Integrating along y -axis, we get A = 2 ∫ 0 π 4 sec ⁡ y - 1 d y = 2 log e sec ⁡ y + tan ⁡ y - y 0 π 4 = 2 log e ⁡ 2 + 1 - π 4 = log e ⁡ 3 + 2 2 - π 2   s q .   u n i t s

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