Evaluating Improper Integrals

[@chris2656]

you have gotten me through my chem and math exams. I don't know what it is about your vids, but they're just so clear. Like when I'm struggling with something I always check for your vids first

[@navjotsingh2251]

These videos are effective because: A) they are simple B) they use nice animations for demonstration C) he shows the necessary formulas This is something a lot of math lecturers fail to do when teaching.

[@robinkovacic8145]

same thing, I was struggling with linear algebra and almost failed my midterms regardless of countless hours of studying. once I discovered his linear algebra playlist, everything changed

[@betterfly7398]

Clear wording & phrasing (every word is accounted for). Clear voice (Doesn't speak too fast, emphasizes important words/phrases). Great Animations.

[@kiwisorbet]

Excellent and clear content. You have helped me go through calc 1 with a horrible teacher. You're always the first one I reach to when I need to learn Calculus. When I graduate and find a job, I'll for sure donate you 30$ for helping me so much in my studies.

[@Divine_Discoveries]

did you graduate and in what field what are you doing?

[@kiwisorbet]

@@Divine_Discoveries haven't graduated yet, but I'm in my second year into my electrical engineering bachelors

[@rozhinaraoufi8545]

professor Dave, you are the light of my life

[@anysianas5099]

You make me love maths more and more your explanations are so clear easy to understand prof Dave thank you 🙏🏾

[@daisyg509]

Thank youuuu. I have seen this in calc 2, audited calc 2 and still didn't understand UNTIL I watched this video. This was one of the few calc 2 concepts I did not understand well.

[@egelsia7009]

Hey Proffessor, I have an exam next week and you made me understood nearly all of the subjects. Thank you for everything, have a nice year ♥

[@heeberman]

Loved your explanation for the arctan limit. This was a confusion I had from a lecture last night and I just stumbled upon this in your video serendipitously.

[@bernardnyarkoh1798]

Waaaw, Professor you have really enlightened my understanding. God bless you

[@hoangvietphu8467]

i love your math videos please make them more regularly!

[@matemaatika-math]

If you pay him more regularly he has more options to buy time for making videos more regularly. Or we can make it possible for him and why not for everyone to get free access to all the necessary resources.

[@kimberlyhoang5191]

i like how you went in depth about certain parts. It was very easy to understand.

[@JesusMartinez-zu3xl]

wow! You explained this concept better than my cal instructor in 13 minutes! Thank you!

[@bathtubanarchy]

6:10 I don't recall seeing this common integration mentioned before?

[@Pochix2024]

You are truly a savior Prof Dave♥️

[@graced4844]

subscribing because even though my calculus prof teaches fine, we go way too fast and i always need help. thanks dave!

[@derplerp8412]

I have an exam tmr and my teacher is not the greatest but because of you I might do well now

[@Kiky_MedPhysicist]

Thank you sir for your dedication and for making this free! 🙏

[@IronMan-di3zi]

Sir your explanation is great. I especially liked the way you taught here with geometrical interpretation which I was looking for ❤️❤️ Thank you sir for this amazing content

[@gilesrobinson4066]

This explanation was a lot better than the one at my uni, thanks

[@schifoso]

Excellent examples.

[@goducksgo613]

Yes, the one where the area was pi blew up my mind

[@katherynew]

Excellent simplification of this rather nebulous concept complicated by wordy textbooks!

[@issacoh8675]

Quick question: At 9:34, shouldn't the bounds be changed since you are using u-substitution. I know that they will change back after that step, but for that specific step, shouldn't the bounds be different or are they supposed to stay the same?

[@michaellee7778]

The bounds should be different. The upper bound will become 3 (since x - 2 = u , 5 - 2 = 3) and the lower bound becomes t - 2.

[@calebknight8213]

I believe the reason he didn’t change the limits of integration is because he substituted x-2 back in for u after taking the integral. Normally with u-sub on definite integrals you don’t plug your original substitution back in, so you need to change the limits with respect to u. Because he changed his function back to x values, there was no need to change the limits of integration.

[@SurajKumar-ey2et]

5:15 i didn't understand what he meant by saying " One over x squared gets small enough fast enough that the area under the curve is finite, while one over x also gets small enough, as it too, goes to zero as x approaches infinity, it just doesn't do it fast enough "

[@spnfangirl67]

thanks professor dave you're the best!

[@matemaatika-math]

I hope that this time you wouldn't argue that there's a part that needs to be corrected at 11:39: You must put parenthesis around 3 * t ^ 3 as otherwise, t ^ 3 would be part of the nominator or whatever you English-speaking crowd call the fraction part or the part that's on top of the fraction line. According to your notation we can read -1 / 3 * t ^ 3 === -t ^ 3 / 3.

[@michelsupply5328]

SIr Love from India,,,,,,,,,,,,,, Sir i was doubt on this topic but still i understood perfectly...............

[@ilovecalculus2807]

Yay! Thank you very much.. May God bless you and your family.

[@OwlFatherTarnished]

Bro an absolute life saver

[@payalsagar1808]

crystal clear explanation🙌

[@utilizator1701]

9:36 you have forgotten to change the limits of the integral (it should be from t-2 to 3).

[@dangyo962]

true but it doesn't matter because he switched u back into x - 2

[@brunomartel4639]

in 5:14 you forgot to put the limit of t that tends to inf in the rhs

[@codexhd8689]

Nice explanation. Watching from zambia

[@asema.1484]

love this guy he is briliant

[@vaiterius]

Who made your intro sequence? it is legendary

[@ian.ambrose]

He made it himself. He is an animator too.

[@mrhunterai...331]

Just came across this channel if you want to master calc I 100% recommend you watch it.

[@tenma628]

its 12am and i have a calc exam tmrw im not prepared for. thank u for this video

[@Schlohmotion]

11:33 dx/x^4 .... does this stand for 1/x^4 dx ?

[@ProfessorDaveExplains]

yep same thing!

[@Schlohmotion]

@@ProfessorDaveExplains Professors seem to answer faster than teachers, neat! Thank you.

[@LaGGSBD]

8:13 couldn't you get 360 as the result if you used degrees instead of radians?

[@ProfessorDaveExplains]

we always use radians in such a context because pi is a value that makes sense in terms of an area whereas degrees do not. also, pi is 180 degrees anyway.

[@acutespike9260]

btw how can we know that we should use improper integral without drawing the graph? :D

[@kris-yg9om]

Revolutionhk4 when you need to calculate the area between an asymptotic value and a real and definable x value, same applies to the y axis if you function Has horizontal asymptote

[@flamingturkey7727]

Use this method whenever there’s an improper integral. Essentially, it’s improper whenever the bounds include infinity or negative infinity or when there’s a vertical asymptote (you should know from many other math classes that if there’s an x value that would make the denominator 0 then there’s a vertical asymptote there.)

[@oshawastaken]

DAVE U ARE A GODSEND

[@hellboy4167]

You are still saving your students degree😭💯

[@veliamomo6561]

Great Teacher, thank you

[@jursamaj]

It should not be surprising that the integral of 1/(1+x^2) is convergent. Over the span from 0 to 1, it clearly has a finite area. Meanwhile over the span 1 to ∞, it is always less than 1/x^2, which is convergent.

[@bikram_kumar]

We can use the L'Hospital's Rule for evaluating the limit, instead of checking the graph for the limit values ;)

[@bobthebb-illder827]

8:28

[@suyogadhikari2349]

This video is amazinggggg!!

[@yagzyalcntas553]

how about partial integration for improper integrals? the uv part is calculated using the limits? or just left as it is?

[@edison9581]

Hi professor, how come the solution of tan^-1(0) is not 0 + n(pi), but is just 0?

[@hana29971]

I think that's because we only take the minimum values and if we write it as n(pi) it might complicate the results

[@esramazlan7445]

Thanks sir

[@nirajkc224]

So cool professor

[@audioadhd]

I sing the jingle involuntarily

[@shikhadwivedi2737]

Uss

[@zeinabmohamed1668]

استفدت جدا الحمد الله

[@Vagdebrume]

You're still awesome :)

[@Vagdebrume]

And video is a really good way to teach maths :)

[@freefiregamer-st5wu]

sir you are from which country?

[@ProfessorDaveExplains]

USA

[@s-semane]

i have many questions anyway!

[@tunabozkurt5578]

I love this guy 😝

[@elamvaluthis7268]

Very nice explanation 😂🤣🤣😄🙏👍.

[@farrukhsaif108]

Here for a math calc 1 uni exam

[@brxyann]

Legend

[@matemaatika-math]

Here at 6:18, you're using ambiguous notation again as also Krista King does however I remember her mentioning that one must be sure of the context before reading. So if you use -1 for arcustangens then your saying can be interpreted as cotangens as well. I suggest to write directly arctan and not using the inverse notation. I suggest arctan and even not atan as I've seen you using atan earlier in the meaning of a * tan as you told me that multiplication was implied on adjacent terms. How in our holy green world can we know that you mean tangent and not three terms t, a and n which are multiplied together? Because nobody past like fourth degree of something thinks that way?

[@jumanahabiballa6258]

Thankss Dave 😏

[@Meowhoraga420]

😩

[@rojaponduru4106]

Please say easily

[@ProfessorDaveExplains]

this is as easy as it gets, bud!

[@matemaatika-math]

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[@ian.ambrose]

Thank you Jesus Dave Professor.

[@TheLilLebs]

i love you

[@dennisemacapagal4331]

From chemistry jesus to mathematics/calculus jesus

[@matemaatika-math]

I've found yet another ambiguous notation, this time a verbal one at 7:38. It's hilarious that we get a whole pie altogether however what we get here, isn't a pie but it's a something that you represent with a Greek letter that will be pronounced as "pee", so half-pee and half-pee are a whole pee and if we want to illustrate that area we could color is after pee as it's full of pee. But whose pee is blue? Because it's a blueberry pie.

[@apurbasharma]

you are fucking amazing

[@payalsagar1808]

just mazing:)😘

[@GavenYurisich-nu5zn]

A bandai

[@dailyrosesofholyquran780]

👍

[@SurajKumar-ey2et]

5:15 i didn't understand what he meant by saying " One over x squared gets small enough fast enough that the area under the curve is finite, while one over x also gets small enough, as it too, goes to zero as x approaches infinity, it just doesn't do it fast enough

[@celinejeni5629]

nc sir

[@davethesid8960]

But pi isn't finite! 🙄

[@ProfessorDaveExplains]

Um, yes it is.

[@davethesid8960]

@@ProfessorDaveExplains Wow, thanks for replying, I was just saying that although it IS a finite value, it cannot be written out at its full capacity... Eh, as kind of a joking around

[@ProfessorDaveExplains]

Ah, yes, it's irrational.

[@davethesid8960]

@@ProfessorDaveExplains And also thanks for such a clear explanation about integration. Your way of teaching is just sooo different (in a positive sense) from plain old scholar education, I love it! ❤

[@davethesid8960]

@@ProfessorDaveExplains Actually I'm so keen on maths that I decided I would like to become a maths professor one day too, hope I'll achieve this goal.

[@IbrarKhan-fb9ze]

Thanks sir