Average temperature question

[dannatyler]

I'm hoping someone could guide me with this one b/c I don't even know where to start.

Suppose the temperature in degrees Fahrenheit of a metal bar of length 2 feet depends on the position x according to the function T(x)= 40 +20x(2-x). Find the average temperature in the bar.

Thanks all!

 

[galactus]

This looks to be an 'average value of a function over an interval' problem.

Try using

\(\displaystyle \frac{1}{b-a}\int_{a}^{b}f(x)dx\)

 

[dannatyler]

Thanks thats what I thought but I just was sure what the integral would be from. Would it be from 0 to 2?

 

[BigGlenntheHeavy]

\(\displaystyle Average \ Temperature \ = \ \frac{1}{2}\int_{0}^{2}T(x)dx \ = \ 53\frac{1}{3}^0 F\)