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JEE Main202524 Jan 2025Evening ShiftMathematicsArea Under CurvesActual

The area of the region enclosed by the curves y= e ^x, y= | e ^x-1 | and y -axis is:

Options

  1. A1- _ e 2
  2. B_ e 2
  3. C1+ _e 2
  4. D2 _e 2-1

Correct answer

A. 1- _ e 2

Step-by-step solution

aligned & e^x=1-e^x 2 e^x=1 & e^x= 1 2 & x= 1 2 & _ (1 / 2) ^0 [e^x- (1-e^x ) ] d x & = _ 2 ^0 (2 e^x-1 ) d x=2 e^x- .x |_ - 2 ^0 & =2-(1+ 2) & =1- _e 2 aligned

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