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BITSAT2017MathematicsArea Under CurvesActual

The area under the curve y = cos x - sin x , 0 ≤ x ≤ π 2 and above X -axis, is

Options

  1. A2 2
  2. B2 2 - 2
  3. C2 2 + 2
  4. D0

Correct answer

B. 2 2 - 2

Step-by-step solution

Required area = ∫ 0 π / 2 cos x - sin x d x = ∫ 0 π / 4 cos x - sin x d x + ∫ π / 4 π / 2 sin x - cos x d x = sin x + cos x 0 π / 4 + - cos x - sin x π / 4 π / 2 = 2 - 1 - 1 - 2 = 2 2 - 2

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