Question

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

Answer 1

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^(x/2) dx`, between the limits `0` and 2.

The integral is`[2e^(x/2)]` between the limits

= `2(e-1)`.

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