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MHT CET202124 Sep 2021Evening ShiftMathematicsArea Under CurvesActual

The area of the region bounded by the curve y=2 x-x^2 and X -axis is

Options

  1. A2 3 sq. units
  2. B4 3 sq. units
  3. C5 3 sq. units
  4. D8 3 sq. units

Correct answer

B. 4 3 sq. units

Step-by-step solution

Point of intersection of curve y=2 x-x^2 and x axis, is 0=2 x - x ^2 x ( x -2)=0 x =0,2 When x =0, y =0 and when x =2, y =0 Refer figure Required area is shaded aligned & A= ₀^2 (2 x-x^2 ) d x & =2 [ x^2 2 ]₀^2- [ x^2 3 ]₀^2 & =(4)- ( 8 3 )= 4 3 aligned

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