# What is the area of the region in the first quadrant by the graph of y=e^(x/2) and the line x=2?

Mar 30, 2016

2e-2 = 3.4366, nearly. See the graph for this area.

#### Explanation:

The line x = 2 is parallel to y-axis.

The area in ${Q}_{1}$ is bounded by

the curve, x = 0, x-axis and x = 2. See the graph.

Area = $\int {e}^{\frac{x}{2}} \mathrm{dx}$, between the limits $0$ and 2.

The integral is$\left[2 {e}^{\frac{x}{2}}\right]$ between the limits

= $2 \left(e - 1\right)$.

graph{(x-2ln y)(2-x)(x)=0[0 2] [0 2.72]}