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COMEDK2018MathematicsArea Under Curves

The area of the region bound by the curves y=x² and y=4 x-x² is

Options

  1. A16 3 sq. units
  2. B8 3 sq. units
  3. C4 3 sq. units
  4. D2 3 sq. unit

Correct answer

B. 8 3 sq. units

Step-by-step solution

Given equation of curves are y=x² and aligned y &=4 x-x² y-4 &=-4+4 x-x² y-4 &=- (x²-4 x+4 )=-(x-2)² aligned Now, required area = ₀² (4 x-x² )-x² d x aligned &= ₀² (4 x-2 x² ) d x . &= [2 x²- 2 3 x³ ]₀² &= [ (8- 16 3 )-0 ] &= 24-16 3 = 8 3 sq. units aligned

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