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BITSAT2015MathematicsArea Under CurvesActual

The area of the region R = (x, y):|x| |y| . and x² .+y² 1 is

Options

  1. A3 8 sq units
  2. B5 8 sq units
  3. C2 sq units
  4. D8 sq unit

Correct answer

C. 2 sq units

Step-by-step solution

Required area =4 (Area of the shaded region in first quadrant) =4 ₀^ 1 2 (y₁-y₂ ) d x=4 ₀^ 1 2 ( 1-x² -x ) d x =4 [ x 2 1-x² + 1 2 ⁻¹ x- x² 2 ]₀^ 1 / 2 =4 [ 1 2 2 1 2 + 1 2 4 - 1 4 ]=4 [ 1 4 + 8 - 1 4 ]= 4 8 = 2 sq units

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