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Manipal MET2013MathematicsArea Under Curves

The area of the figure bounded by the parabola (y-2)^2=x-1 , the tangent to it at the point with the ordinate 3 and the x -axis is

Options

  1. A3
  2. B6
  3. C9
  4. DNone of these

Correct answer

C. 9

Step-by-step solution

Given parabola, is (y-2)^2=x-1 d y d x = 1 2(y-2) when, y=3, x=2 d y d x = 1 2(3-2) = 1 2 Tangent at (x, 3) is y-3= 1 2 (x-2) x-2 y+4=0 Required area ₀^3 (y-2)^2+1 d y- ₀^3(2 y-4) d y= [ (y-2)^3 3 +y ]₀^3- [y^2-4 y ]₀^3= 1 3 +3+ 8 3 -(9-12)=9 .

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