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JEE Main 24-Jan-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 24-Jan-2025 Paper - Shift 24 Marks
MCQ
The area of the region enclosed by the curves $\mathrm{y}=\mathrm{e}^{\mathrm{x}}, \mathrm{y}=\left|\mathrm{e}^{\mathrm{x}}-1\right|$ and y -axis is:
  • A
    $1+\log _{\mathrm{c}} 2$
  • B
    $\log _{\mathrm{e}} 2$
  • C
    $2 \log _{\mathrm{c}} 2-1$
  • ✓
    $1-\log _{\mathrm{e}} 2$
✓

Answer

Correct option: D.
$1-\log _{\mathrm{e}} 2$
(D)
Sol.

Image
For Area $\int_{-\ln 2}^{0}\left[e^{x}-\left(1-e^{x}\right)\right] d x$
$\int_{-\ln 2}^{0}\left(2 e^{x}-1\right) d x=\left[2 e^{x}-x\right]_{-\ln 2}^{0}$
$=(2-(1+\ell \mathrm{n} 2))$
$=1-\ln 2$

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