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MHT CET202312 May 2023Morning ShiftMathematicsArea Under CurvesActual

The area of the region bounded by the curves y= e ^x, y= x and lines x=1, x=2 is

Options

  1. A( e -1)^2 sq . units
  2. B( e ^2- e +1 ) sq . units
  3. C( e ^2- e +1-2 2 ) sq . units
  4. D( e ^2+ e -2 2 ) sq. units

Correct answer

C. ( e ^2- e +1-2 2 ) sq . units

Step-by-step solution

aligned & Required Area & = ₁^2 ( e ^x- x ) d x & = [ e ^x ]₁^2- ₁^2 1 x ~d x & = ( e ^2- e )- [x x- ₁^2 1 ~d x ] & = ( e ^2- e )-[x x-x]₁^2 & = ( e ^2- e )-[(2 2-2)-(1 1-1)] & = e ^2- e -(2 2-2-0+1) & = e ^2- e -(2 2-1) & = ( e ^2- e +1-2 2 ) sq. units aligned

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