calculate the following area. first draw a neat sketch indicating the required area. y=2e^(2x)

Question

The enclosed by y= 2e^2x , the x-axis, x= 0 and x= 2

Answer 1

The area is the integral of ydx, so this is the same as 2e^(2x)=e^2x between the limits 0 and 2: e^4-1=53.6 approx.

Sorry for delay in sending picture. (e^4=54.6, e^0=1)

Answer 2

The region is that under the graph of 2e^(2x) from x = 0 to x = 2,

So it is the integral from 0 to 2 of 2e^(2x) dx.

This is 2e^(2x)/2 evaluated from 0 to 2,

Or e^4/ – 1

=53.6

Also understand about How to Graph Special Functions