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28 August, 01:08

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

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  1. 28 August, 01:35
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    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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