Improper Integrals: How to Integrate with Infinities, 2 ways!

Improper integrals let's us integrate function when infinity is involved. This could come about because of an infinite domain, such as the integral from 1 to infinity of some function. But it can also occur if there is a vertical asymptote in the domain. While we might initially guess anything with infinities results in infinite area, indeed many such regions actually converge to a finite value. To study this we look at so called p-integrals, integrals of functions of the form 1/x^p. Depending on the value of p, these integrals converge or diverge.

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati. #calculus #math

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[VasilevArtem-gu]

started watching these great series. thank you. a comment just for YT algorithms to push them

[a-levelmathstutorials]

Fantastic explanation my man, thanks alot loving all the videos

[pipertripp]

very handy. Teaching myself stats and this was super helpful for computing probabilities of continuous random variables.

[journeymantraveller]

Yes, 1/x^2 is not symmetric about y=x! Legendary presentations. Wish this resource was around when I was an undergraduate, but still enjoying and learning post MSS. CCs would be great.

[cokcury]

Dr. Trefor, thank you for your remarkable work over calculus and let it free on YouTube. It seems that you've established all the basic ideas for a student of calculus through this postes. And all the things are very extordinary.
But can I do perform cell in calculus part with these ideas.
I've finished calculus 1 & calculus 2 of your series. And I found myself visualising the trig functional area under curves while handling integration by parts, and relating domains and using special triangles.

Thanks a lot dr.
And please affiliate adsence to all your videos. And try to earn little more. As you will have to guide us all a long way through math.

Till last week math was a nightmare. But after your classes. I find it to be beautiful.

[albinsopaj]

I think if you were to specify that 1/x is a power series, and for power series you have
a) If p > 1, the series is convergent, hence it has a sum
b) If p ≤ 1, the series is divergent, hence no sum can exist (it is either ± ∞);
maybe it would have made more sense to connect ideas and concepts from different topics. However the explanation was acceptable.

[pravingaikwad]

How do I know if the function is improper or proper??

[donlansdonlans]

I thought that the integral from 2 to infinity of 1/x converged, im kinda dissapointed :(. Anyway, the fact that the integral from2 to infinity of 1/x diverges is related to the fact that the harmonic series diverges?