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Most Important Selected Qs for JEE AdvancedMathematicsArea Under Curves

The area of the region bounded by the curve C: y= x+1 x^2+1 and the line L: y=1 , is

Options

  1. A1- 1 2 2+ 4
  2. B2- 4 +1
  3. C1 2 2+ 4 -1
  4. D2- 2 +1

Correct answer

C. 1 2 2+ 4 -1

Step-by-step solution

On solving C: y= x+1 x^2+1 and the line L: y=1 , we have x+1 x^2+1 =1 x+1=x^2+1 x(x-1)=0 x=0,1 Thus, the points of intersection are at x = 0 and x = 1. Required area = ₀^1 ( x+1 x^2+1 -1 ) d x= 1 2 ₀^1 2 x x^2+1 d x+ ₀^1 1 x^2+1 d x- ₀^1 d x= [ 1 2 ( x ^2+1 )+ ( ⁻¹ x )- x ]₀^1= 1 2 2+ 4 -1

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