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Find the region enclosed by the curves: `y=e^(x)` , `y=xe^(x)` , x=0``

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You need to find the limits of integration, hence, you need to solve the equation `e^x = x*e^x` , such that:

`e^x = x*e^x => e^x - x*e^x = 0`

Factoring out` e^x` yields:

`e^x(1 - x) = 0`

Since `e^x > 0` , hence `1 - x = 0 => x = 1`

You need to evaluate the functions `y = e^x` and `y = x*e^x` at `x = 0` and `x = 1/2` , such that:

`x = 0 => y = e^0 => y = 1`

`x = 0 => y = 0*e^0 = 0`

`x = 1/2 => y = e^(1/2) => y = sqrt e `

`x = 1/2 => y =...

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