SOLUTION: Find the area between the curves. x=-3 x=2 y=4e^4x y=3e^(4x) + 1 ​(Do not round until the final answer. Then round to the nearest hundredth as​ needed.)

Algebra ->  Finance -> SOLUTION: Find the area between the curves. x=-3 x=2 y=4e^4x y=3e^(4x) + 1 ​(Do not round until the final answer. Then round to the nearest hundredth as​ needed.)      Log On


   

Question 1032464: Find the area between the curves.
x=-3
x=2
y=4e^4x
y=3e^(4x) + 1
​(Do not round until the final answer. Then round to the nearest hundredth as​ needed.)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
As shown by the graph, the curves shift at x=0 so break up the integral accordingly.
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A%5B1%5D=int%28%283e%5E%284x%29%2B1-4e%5E%284x%29%29%2Cdx%2C-3%2C0%29
A%5B1%5D=int%28%28-e%5E%284x%29%2B1%29%2Cdx%2C-3%2C0%29
A%5B1%5D=-e%5E%284x%29%2F4%2Bx%2BC
A%5B1%5D=-%281-e%5E%28-12%29%29%2F4%2B%280%2B3%29
A%5B1%5D=11%2F4-1%2F%284e%5E12%29
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A%5B2%5D=int%28%284e%5E%284x%29-%283e%5E%284x%29%2B1%29%29%2Cdx%2C0%2C2%29
A%5B2%5D=int%28%28e%5E%284x%29-1%29%2Cdx%2C0%2C2%29
A%5B2%5D=e%5E%284x%29%2F4-x%2BC
A%5B2%5D=%28e%5E%288%29-1%29%2F4-%282-0%29
A%5B2%5D=e%5E%288%29%2F4-1%2F4-2
A%5B2%5D=e%5E%288%29%2F4-9%2F4
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So then,
A=A%5B1%5D%2BA%5B2%5D
A=11%2F4-1%2F%284e%5E12%29%2Be%5E%288%29%2F4-9%2F4
A=1%2F2%2B%281%2F4%29%28e%5E8-1%2Fe%5E12%29