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Mathematics
Kahlua
23 March, 05:09
Find the area between y=e^x and y=e^2x over [0,1]
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Jensen Patterson
23 March, 06:37
0
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
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