Find the average value of the function g(x)=2sin(x)+e^(x/pi) on the interval [0, 2pi].

Like so:

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g(x)=2 sin(x) +e^(x/pi) on [0,2pi]

A= 1/(2pi -0) \(\int_{0}^{2pi}\)(2 sin(x) + e^(x/pi)) dx

= 1/2pi(-2 cos(x) + pi e^(x/pi))

Then plug in 0 and 2 pi in for X

 2-pi+(1/2)pi(e^2pi -2)

I know how to set it up, just not 100% sure thats the right answer or not.

To get the average value, divide by 2pi:

\(average=\frac{\pi (e^2-1)}{2\pi} \rightarrow \frac{1}{2}(e^2-1)\)

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