Find the area between y=e^x and y=e^2x over [0,1]

Step-by-step explanation:

Just so you see what you are trying to do, the graph shows you what you are given.

Graph

Red: y = e^x

blue: y = e^ (2x)

green x = 1

equations

integral e^ (2*x) = e^ (2x) / 2

integral e^x = e^x

Solution

e^ (2x) / 2 between 1 and 0 equals e^ (*2*1) / 2 - e^0

e^ (2x) / 2 = 7.3891 - 1 = 6.3891

e^ (x) between 1 and 0 equals e^ (1) - e^0

2.7183 - 1

1.7183

The area between 1 and 0 is 6.3891 - 1.7183 = 4.6708