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AP EAMCET202423 May 2024Morning ShiftMathematicsArea Under CurvesActual

If ( , ) is the stationary point of the curve y=2 x-x^2 , then the area bounded by the curves y=2 x, y=2 x-x^2, x=0 and x= is

Options

  1. A3 2+4 2
  2. B3+ 4 6
  3. C3- 4 3 2
  4. D1 2 + 3 4

Correct answer

C. 3- 4 3 2

Step-by-step solution

y=2 x-x^2 For stationary point d y d x =0 2-2 x=0 x=1= Given curves are y=2^ x , y=2 x-x^2, x=0, x=1 aligned & Required area = ₀^1 2^x d x- ₀^1 (2 x-x^2 ) d x & = [ 2^x 2 ]₀^1- [x^2- x^3 3 ]₀^1= 1 2 - 2 3 = 3- 4 3 2 aligned

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