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!

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    $\begingroup$ You want $b-1$ in the denominator, not $1-b$. $\endgroup$ – saulspatz Mar 22 '20 at 22:36
  • $\begingroup$ oops sorry about that $\endgroup$ – P1081 Mar 22 '20 at 22:37
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    $\begingroup$ Now do a change of variable $u=\frac{\pi}{x}$, evaluate the integral and take the limit. $\endgroup$ – Paul Mar 22 '20 at 22:41
  • $\begingroup$ oh, so you mean I should do a u-substitution $\endgroup$ – P1081 Mar 22 '20 at 22:41

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

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

  • $\begingroup$ 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? $\endgroup$ – P1081 Mar 22 '20 at 23:31
  • $\begingroup$ @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 $0$? $\endgroup$ – Eric Towers Mar 22 '20 at 23:33

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