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JEE Math Practice Question

The area of the region enclosed by the curves $y=\mathrm{e}^x, y=\left|\mathrm{e}^x-1\right|$ and $y$-axis is :

  1. A.$1+\log _{\mathrm{e}} 2$
  2. B.$\log _{\mathrm{e}} 2$
  3. C.$1-\log _{\mathrm{e}} 2$
  4. D.$2 \log _{\mathrm{e}} 2-1$

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