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COMEDK2019MathematicsArea Under Curves

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

Options

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

Correct answer

B. 4 3 sq units

Step-by-step solution

We have, aligned y &=2 x-x² y &=- (x²-2 x ) y &=- [(x-1)²-1 ] y &=-(x-1)²+1 (x-1)²=-(y-1) aligned aligned Required area &= ₀² y d x &= ₀² (2 x-x² ) d x &= [x²- x³ 3 ]₀²=4- 8 3 &= 4 3 sq unit aligned

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