Find the average value of the function `f(x)=6x+4e^x` between x=0 and x=2.

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To get the average value of a function in a given interval use the formula:

`f_(avg)=1/(b-a)int_a^b f(x)dx`

Plug-in f(x)=6x+4e^x, a=0 and b=2.

`f_(avg)=1/(2-0)int_0^2 (6x+4e^x)dx`

`f_(avg)=1/2int_0^2 (6x+4e^x)dx`

`f_(avg)=1/2 ((6x^2)/2 + 4e^x)``|_0^2`

`f_(avg)=1/2(3x^2+4e^x)``|_0^2`

`f_(avg)=1/2[(3*2^2 +4e^2)-(3*0^2+4e^0)]`

`f_(avg)=1/2(12+4e^2-4)`

`f_(avg)=1/2(8+4e^2)`

`f_(avg)=4+2e^2`

Hence, the average value of the function of `f(x)=6x+4e^x` in the interval [0,2] is `f_(avg)=4+2e^2` .

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