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Find the area of the region bounded by the graphs of the given equation: y = e^(x - 1),...

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hardguy | eNotes Newbie

Posted September 12, 2013 at 9:39 AM via web

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Find the area of the region bounded by the graphs of the given equation:

y = e^(x - 1), y = x, x = 1, x = 4

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aruv | High School Teacher | (Level 2) Valedictorian

Posted September 12, 2013 at 10:03 AM (Answer #1)

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Given curves are

`y=e^(x-1), y=x , x=1 and x=4`

Let draw its graph

Since curve y=e^(x-1) and y=x intersect each other only at (1,1)therefore  we need to find area bounded by curve y=x ,x=1 and x=4 .

`A=int_1^4ydx=int_1^4xdx`

`={x^2/2}_1^4`

`=(16/2-1/2)=15/2`  units.

 

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