# How do I find the averge value of the function g(x) on the interval [1, + infinity]?

I know how to find the average value of functions on an interval, but I am having trouble finding the average value of this function with the interval going to positive infinity. I tried doing what the hint says, but I'm not sure if I am on the right track. Can anyone suggest anything? Thank You! • You want $b-1$ in the denominator, not $1-b$. – saulspatz Mar 22 '20 at 22:36
• oops sorry about that – P1081 Mar 22 '20 at 22:37
• Now do a change of variable $u=\frac{\pi}{x}$, evaluate the integral and take the limit. – Paul Mar 22 '20 at 22:41
• oh, so you mean I should do a u-substitution – P1081 Mar 22 '20 at 22:41

## 1 Answer

Given the amount of your homework you have posted in the past four hours...

Hint: $$u = \frac{\pi}{x}$$.

• So I solved by first substituting u for pi/x. ThenI evaluated the integral and when I took the limit I got the answer 0. Is this correct? – P1081 Mar 22 '20 at 23:31
• @P1081 : What do you think? Have you checked for the sorts of errors you have seen before? Can you convince yourself, perhaps by graphing $g(x)$ that the answer could plausibly be near $0$? – Eric Towers Mar 22 '20 at 23:33