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MHT CET202013 Oct 2020Evening ShiftMathematicsArea Under CurvesActual

The area of the region bounded by the curve y=4 x-x² and the x -axis is

Options

  1. A16 3 sq. units
  2. B32 3 sq. units
  3. C32 sq. units
  4. D16 sq. units

Correct answer

B. 32 3 sq. units

Step-by-step solution

We have y=4 x-x² When y=0 , we get x(4-x)=0 x=0,4 Required area is shaded. aligned A &= ₀⁴ (4 x-x² ) d x &= [ 4 x² 2 - x³ 3 ]₀⁴= [2 x²- x³ 3 ]₀⁴ &= |2(16-0)- 64-0 3 |= |32- 64 3 | &= 32 3 aligned

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