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

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40