Calculus

Application of Integrals

Medium

applied

The area (in sq. units) bounded between the curves $x=e^y$ , $x=e$ and x-axis in the first quadrant is

$\frac{1-e}{e}$

$\frac{e-1}{e}$

$e-1$

✅ Correct Option: 3

The curve $x=e^y$ meets $x=e$ at $y=1$ and the x-axis is $y=0$ .

Integrating horizontally, Area $=\int_0^1(e-e^y)dy=[ey-e^y]_0^1=(e-e)-(0-1)=1$ square unit.

2026: 18 May Shift 1

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