posted by James on .
find the area of the region enclosed by y=e^2x, y=e^5x, and x=1.
i am having trouble seeing how this region looks like and having problems with how to start the problem in general.
Much help is appreciated.
y = e^2x means e^(2x)
y = e^5x means e^(5x)
The two curves (equations) intersect at x=0, y=1. Then, going in the positive x direction, they diverge. But, the right side of the region is bounded by a line at x=1.
So, find the area from x = 0 to x = 1 under the curve y = e^(5x) then subtract the area under the curve y = e^(2x) from x = 0 to x = 1.
Just to be clear, it is a vertical line at x=1.