The discussion revolves around the convergence of the integral of the function w/(w-2) over the interval [0,5]. Participants are exploring the implications of the discontinuity at w = 2 and how it affects the evaluation of the integral.
The discussion is ongoing, with participants providing guidance on how to handle the improper integral. Some have pointed out that both parts of the split integral must converge for the overall integral to converge. There is acknowledgment of the undefined nature of the logarithmic terms at certain points.
Participants note the importance of evaluating the integral in segments due to the point of discontinuity and the implications of encountering logarithmic terms that approach infinity or are undefined.
Jbreezy said:Homework Statement
integral [0,5] (w/(w-2))
Homework Equations
I just want to know if does not converge or not.
The Attempt at a Solution
∫2(1(w-2)) dw + ∫dw
= 2ln| w-2| + w from 0 to 5. I know about the discontinuity at w = 2.
So is it still ok from me to just evaluate this as normal.
I would get
2ln|3| + 5 - 2ln|-2|
? Is this OK?
If the range of an integral includes a point where the integrand is undefined then you must be careful. The integral as a whole is undefined if there is any subrange on which it is undefined.Jbreezy said:Confused to I evaluate ∫2(1(w-2)) dw + ∫dw from [0,2] then again from 2 to 5? The whole thing right?
Yes, if I understand your garbled question. This integral--Jbreezy said:Confused to I evaluate ∫2(1(w-2)) dw + ∫dw from [0,2] then again from 2 to 5? The whole thing right?