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NDA2016MathematicsArea Under CurvesActual

What is the area bounded by the curves |y|=1-x^2 ?

Options

  1. A4 3 square units
  2. B8 3 square units
  3. C4 square units
  4. D16 3 square units

Correct answer

B. 8 3 square units

Step-by-step solution

Since |y|= array cc y & y 0 -y & y 0 0 & y=0 array . For y 0 y=1-x^2 For y 0 y=x^2-1 For y=0 x= 1 So area under the curve =4 Area under the region OABO (symmetry) aligned = & 4 ₀^1 1-x^2 dx & .=4 [x- x^3 3 ]₀^1 ] aligned =4 (1- 1 3 )=4 2 3 = 8 3 sq. units

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