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**delgeezee** An arched shaped monument is 570 ft high and has a 600 ft base. It can be modeled by the function$\displaystyle y=1140-285(e^{0.00439x}+e^{-0.00439x})$ where the base of the arch is[-300,300] and x and y are measured in feet. Find the average height of the arch above the ground.

I was able to do this but it took a while. What is the best way to to do this so I dont have to enter too many buttons on my calculator which personally increases my rate of error.

My questions: 1. Can I use **ln** on the integrand and what would it look like? 2. How do I deal with symmety for a LN()?

$\displaystyle y=1140-285(e^{0.00439x}+e^{-0.00439x}) $

$\displaystyle avg value =\frac{1}{600}\int_{-300}^{300}(1140-285(e^{0.00439x}+e^{-0.00439x})) dx$

factor out 285 and distribute the minus sign

$\displaystyle avg value =\frac{1}{600}*285\int_{-300}^{300}(4-e^{0.00439x}-e^{-0.00439x}) dx$

Can I use a Natral Log? and does it look like this???

$\displaystyle LN(avg value) = LN[\frac{285}{600}]\int_{-300}^{300}(ln4-0.00439x+0.00439x)dx $

Specifically, I want to know do I use LN on the **factored** out numbers and the **avgvalue**?

If all is well then My next step would be to split up the intrgrand and check for symmetry. If I didnt previously apply the Ln, then all of the integrand was an even functon. It appers that $\displaystyle e^x$ is an even function but what about LN(x)

ln(-x)= no bueno