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KCET2008MathematicsArea Under Curves

The area of the region bounded by y=2 x-x² and the x -axis is

Options

  1. A8 3 sq unit
  2. B4 3 sq unit
  3. C7 3 sq unit
  4. D2 3 sq unit

Correct answer

B. 4 3 sq unit

Step-by-step solution

Given curve is y=2 x-x² or (x-1)²=-(y-1) The curve cut the x -axis at (0,0) and (2,0) . Required area = ₀² y dx aligned &= ₀² (2 x-x² ) d x= [x²- x³ 3 ]₀² &=4- 8 3 = 4 3 sq unit aligned

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