COMEDK2018MathematicsArea Under Curves
The area of the region bound by the curves y=x² and y=4 x-x² is
Options
- A16 3 sq. units
- B8 3 sq. units
- C4 3 sq. units
- 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