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NDA2019MathematicsArea Under CurvesActual

What is the area of the region enclosed between the curve y^2=2 x and the straight line y=x ?

Options

  1. A2 3 square units
  2. B4 3 square units
  3. C1 3 square units
  4. D1 square units

Correct answer

A. 2 3 square units

Step-by-step solution

y^2=2 x, y=x aligned & y^2=2 x & y=x & x^2=2 x & x=0,2 & Area = ₀^2( 2 x -x) d x & = [ 2 x^3 - 3 2 - x^2 2 ]₀^2 & = ( 4 3 / 2 - 4 2 )-0 & = 8 3 -2= 2 3 sq. unit aligned

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