Comparison test for improper integrals example 2, calculus 2 tutorial

Learn how to use the comparison test to determine if an improper integral converges or not.
We will do the integral of x^2/sqrt(x^5-1) from e to infinity. The 3 steps to use the comparison theorem for improper integral: what you know, do the check, and draw the conclusion!
Check out example 3: • Comparison test for im...
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[@williampattison6628]

I need more teachers like you. You explain things a lot better than a large majority of the teachers that I have had in the past

[@jayyyalldayyy]

I've watched a few videos on the comparison test and yours are by far the most helpful ! thank you 😊

[@mohammedaamir9582]

Thanks, amazing teaching!

[@andreamonteroso8586]

good thing blackpenredpen and youtube exist

[@larissa8232]

Thank you thank you thank you omg thank you SO much

[@juanjosemiguel6966]

I tried to integrate that function, but i could not. I putted into Wolfram Mathematica and the result was longer than expected. Clearly this integral isn't very easy to resolve, true?

[@rafiihsanalfathin9479]

Juan José Miguel well thats called divergent :)

[@ladyanne4294]

hey btw you have really helped me alot.thank u

[@vivellywang4037]

ok，take your time Thanks. Take care

[@princessmalobola8378]

And he's sooo funnny :-)))))!!!

[@luyandamolala1108]

Wola mzukulu ka Chan

[@vivellywang4037]

How do they get linearly independent on (-Infiniti, Infiniti) ? Please upload some videos if you can. If you can't, it's ok. I did research on KZbin, I couldn't find one good video. Thank you so much tho. Take care. I've been watching your videos since spring 2016. You are the best.

[@ncedonqeto9107]

What happens when the inequality is false , say the the integral you start with ( the know) is covergent and you work that until you see that the inequality does not hold true , would that mean the improper integral is divergent ?

[@blackpenredpen]

check out example 3 kzbin.info/www/bejne/a3izamlpoLWmhqc

[@DestinyQx]

i love your videos! (side note: slight error at 6:10 ? shouldn't it be x^5 ≥ x^5 - 1 ? same conclusion though in the end)

[@blackpenredpen]

DestinyQx yea. I didn't square both sides tho. I just rewrote the 5/2 power with sqrt lol

[@DestinyQx]

thanks for videos! i began studying diff eq because of your vids.. maybe one day i'll study linear algebra too

[@blackpenredpen]

kzbin.info/www/bejne/a3izamlpoLWmhqc

[@I_make_countless_mistakes]

i thought it would be 2 instead of 1at 3.15 Since a =2

[@qwerasdfqe]

what would you do if the equality check gives you false?

[@NotYourAverageNothing]

It has no elementary solution.

[@vivellywang4037]

Can you do some differential equations?

[@blackpenredpen]

vivelly wang I am uploading, some second order and reduction of orders. What topics did u have in mind?

[@vivellywang4037]

blackpenredpen thank you. I'm working on homogeneous second order linearly dependent and linearly independent. I knew all the basic stuff, but some books wrote really hard theorem. I don't understand. It's about f(t)=t^2 if t=0 and g(t)= 2 t^2, if t= 0 are linearly independent on (-Infiniti, +infiniti). I only understand they are linearly dependent on (-infinit, 0) and (0, + Infiniti).

[@blackpenredpen]

vivelly wang vivelly wang hi vivelly. It's really late now and I prob won't be able to be in school this weekend to make more videos. But the way to do that is, since t^3 and 4t^4 are linearly independent, thus those two piecewise functions are overall linearly independent.

[@blackpenredpen]

Perhaps you have a theorem like this in the book, which says if W(f,g) is not zero at some x_0 on the interval I, then f and g are linearly independent on I

[@blackpenredpen]

Thus u can show that W(x^3,4x^4) is not zero on (0 to inf) thus f and g are L.I.

[@user-nl7mn4rr6s]

我覺得右邊的寫法有點讓誤解：第一條式子並不需要大於等於零，零只是一般來說方便驗證，只要是有限大的數就可以。第二條式子小於零也可以類似地用，只是不等式方向要相反。與第一式相同地，這也不必需是零。

[@elixiroflife9636]

mu test will be much easier

[@parthasarker6121]

Well, you can leave out some details which are obvious in the process