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MHT CET202121 Sep 2021Morning ShiftMathematicsArea Under CurvesActual

The area of the region bounded by the curve y^2=4 x and the line y=x is

Options

  1. A8 3 sq. units
  2. B5 8 sq. units
  3. C3 8 sq. units
  4. D3 5 sq. units

Correct answer

A. 8 3 sq. units

Step-by-step solution

Refer figure, point of intersection of given curves are x ^2=4 x x ( x -4)=0 O (0,0) and P (4,4) Required area is shaded. aligned & A= ₀^4( 4 x -x) d x=2 ₀^4 x^ 1 2 d x- ₀^4 x d x & =2 [ x^ 3 2 ( 3 2 ) ]₀^4- [ x^2 2 ]₀^4- ( 4 3 )(4 2)- 16 2 & = 32 3 - 16 2 = 16 6 = 8 3 sq. units. aligned

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