# Improper integral

Thread starter 1 month ago
#1
If both limits are improper such as undefined at 0 to infinity how would I write out the integral. Should I split the integral?
0
1 month ago
#2
(Original post by Student 999)
If both limits are improper such as undefined at 0 to infinity how would I write out the integral. Should I split the integral?
Can you post an example? I don't think you necessarily have to "split" the integral - just be aware that you may need to write 2 separate limiting processes at the end e.g. lim (a->0( for the lower limit and lim(b->inf) for the upper limit, provided you can evaluate the indefinite integral and then take limits.

Care must be taken when there is a discontinuity within the integration range however.
0
Thread starter 1 month ago
#3
I see, I'm stuck at the end of this question could you help, thanks
(Original post by davros)
Can you post an example? I don't think you necessarily have to "split" the integral - just be aware that you may need to write 2 separate limiting processes at the end e.g. lim (a->0( for the lower limit and lim(b->inf) for the upper limit, provided you can evaluate the indefinite integral and then take limits.

Care must be taken when there is a discontinuity within the integration range however.
0
1 month ago
#4
(Original post by Student 999)
I see, I'm stuck at the end of this question could you help, thanks
I have to admit being a bit rusty on this, but a quick google suggests that the inverse hyperbolic cotangent (arcoth) is only defined on the union of 2 open intervals (-inf, -1) and (1, +inf), so you're not going to get a meaningful result with 0 as the lower limit of integration!

Where have you got this question from? Is is supposed to have a finite answer?
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