Calculus 2 improper integrals (10 examples)

If Type 1 Improper Integral Converges, Then Type 2 _______?
Calculus 2 improper integrals, File: bit.ly/3nilo3c
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0:00 5 Round of Improper Integral Battles
0:05 Q1, integral of 1/(2x-1) from 1 to inf vs. from 1/2 to 1
3:55 Q2, integral of 1/(x^2+x-2) fro 2 to inf vs. from 1 to 2
*small mistake, thanks to Pedro for pointing out: at 11:56 should -(1/3)(ln4)*
12:36 Q3, integral of 1/sqrt(x^2-1) from 2 to inf vs. from 1 to 2
19:19 Q4, integral of 1/(x*sqrt(x^3-1) from 2 to inf vs. from 1 to 2
27:40 Q5, integral of tan(x) fro 0 to inf vs. from 0 to pi/2

[@pedromello5854]

11:56 -(1/3)(ln4)

[@blackpenredpen]

Ah, thanks! A small mistake and lucky it didn't affect the answer.

[@michaelwpannekoek]

@@blackpenredpen looks correct to me? I don't see where the mistake was first made

[@blackpenredpen]

I forgot the neg in the video

[@HeyKevinYT]

12:22 I’d also like to point out that we’re taking the ln abs. value of -♾, so with coefficient -(1/3), the final answer should be -♾ (I think!!) but I it doesn’t matter because the answer diverges anyway Edit: nevermind ignore this I’m wrong lol

[@nuklearboysymbiote]

@@HeyKevinYT good catch, this might affect the answer

[@mooblerthomson9851]

Thank you so much for making these videos I love calculus and anytime I’m stuck you are always the first place I check for explanations. The way you explain things is so easy to understand and you always show tricks and short cuts that I’ve never been taught in class that are immensely helpful.

[@bleddyndavies4935]

I love you bprp, cause of your channel I got a deeper interest in Maths and have signed up for the UKMT mentoring scheme

[@blackpenredpen]

Thank you. I am glad to hear. Could you tell me more about the UKMT program? What is it?

[@bleddyndavies4935]

@@blackpenredpen It's a programme where school students (I'm 17) can be assigned a mentor and get sent problem solving questions every month, then over the month you complete the questions are write your solutions, and send them to your mentor at the end of the month, then receive the answers a few days later. You can find out more here: www.ukmt.org.uk/enrichment/mentoring-scheme You would likely find these pretty easy, but I think they're pretty challenging. Maybe you could do a video about some of them for your younger, pre-university audience?

[@lolQ459]

Bleddyn Davies is it free? Can a nonstudent get involved?

[@bleddyndavies4935]

@@lolQ459 I'm fairly certain that it is free, yeah. I'm not sure if it's just students or not, but I don't think it is. You'd have to check the website, sorry

[@pinklady7184]

Bleddyn Davies yeah, why can't we kidnap bprp and clone his brain for implants? 😁

[@nikolacatic9549]

Man thank you for sharing your knowledge with us. Thanks to your integrals and derivates I got into Faculty of Technical Sciences. I bow to you!

[@zrksyd]

7:00 I actually thought of (x-1)/(x+2) as 1 - (3/(x+2)), which approaches 1 - 0 as you go to infinity. I feel like that's easier to explain that L'opital's rule.

[@cosmo1413]

Reminds me of the old integral battles, so cool!

[@blackpenredpen]

They are integral battles! : )

[@waywalker713]

We need more tricky Integrals🤓

[@omshandilya8888]

i also want to become a mathematician like you watching this at 2AM

[@Ken-no5ip]

3 am gang, having my head explode with new integral techniques

[@Visputescooking]

1:50 I love that as WELL!

[@Silvar55x]

You can also do: ln(1/4) = ln(1) - ln(4) = 0 - ln(4) = -ln(4)

[@stigastondogg730]

When you get to the final answers in your videos I feel compelled to applaud

[@nicogehren6566]

great questions Mr.bprp thanks from Brazil

[@turtlellamacow]

The third one is easier and cleaner with the change of variable x = cosh(u), but I don't know if hyperbolic functions are part of your curriculum. Of course the answer, arccosh(2), is the same numerically.

[@blackpenredpen]

turtlellamacow That will be at the end of the semester, after I cover the parametric equations.

[@srnjnmedhi]

Seriously, blackpenredpen is one of my favourite KZbinrs.

[@jonathanweihing9650]

24:58 arctan(squareroot(3))=pi/3

[@blackpenredpen]

Excellent!!

[@jessehammer123]

Paulo Ricardo To keep arctan a function, we only define it on the interval of tan from -pi/2 to pi/2. Otherwise, we’d have several outputs, which would make arctan not a function and destroy its usefulness.

[@ashtonsmith1730]

@@jessehammer123 plus it doesnt matter which interval you use (like 0 to pi)

[@appanraj880]

I love your videos madly

[@lucasvic7010]

Nice, Thanks very much. It is very helpful.

[@rodricrack1072]

Please, someone. What are the songs names (the 0:00 is the most important to know)? Thanks

[@josebeleno1213]

Hi. I have a question in the integral of tan(x) from 0 to infinity. I have learned that if you integrate from [a,b] and there´s a vertical asymptote at c where a

[@AnimeMemesDaily]

great video

[@luiseduardoortizortiz860]

About the first integral battle, I did it but I got (1/2)*Ln|x-1/2| instead (1/2)*Ln|2x-1|, I derived them and the result was the same in both cases. I wonder if they are two different functions why both of them are integral of the same function? Greetings from Colombia

[@naufaladityajuniarahman8642]

Can you tell me how to solve integral of (1+(xsin(x))^2)^(1/2), it's for search arc length from sin(x)-xcos(x), 0 to phi

[@diffusegd]

Evaluate integral of e^-(x^4) from -infinity to +infinity

[@Fun_maths]

Interesting

[@GSHAPIROY]

Another small mistake, at 16:39, you forgot to close the absolute value.

[@hamiltonianpathondodecahed5236]

infinity leaked out anyway

[@LuVD990]

💯, what have you study?(for example, engineering. I do not know, sorry)

[@Arpan.Das.]

I'm from India 🇮🇳. Your video is very helpful for me.

[@abdellh8079]

I get confusing to know why you put at the last of the equation integral the dx, I talk about the first line that you had written

[@Dhanush-zj7mf]

At 3:23 what if it was approching 0 from left hand side then ln|0-| would if approach +infinity. I am student please help me..

[@ashtonsmith1730]

ln(x) isnt defined when x

[@Daniel-ef6gg]

(x-1)/(x+2) = (x+2-2-1)/(x+2) = 1 - (3/(x+2)). When x->inf, this just goes to 1.

[@noahdunning6258]

I was just doing these today lol

[@theunkown2982]

Keep goin

[@Elfango]

Epic

[@integralboi2900]

Didn’t you do this on your second channel?

[@blackpenredpen]

Yea. This is the main video. Those are meant to be the HW sol for my students.

[@omshandilya8888]

2020 raise to the power 2019 - 2020 divided by 2020 square + 2021=N then find the sum of digits of n bro plz solve this?? trying from last 5 weeks

[@executorarktanis2323]

Can you try doing any topology and I am also concerned about the end you took a long long sigh

[@einsteingonzalez4336]

I thought all Type 2 integrals diverge...

[@warrickdawes7900]

Did BPRP swear at 28:27???

[@Jared7873]

No

[@abdellh8079]

I don't make out anything , I should have back to lean maths again

[@vinay9477]

What were you about say at the end.... When you said..."and..." Video stopped Was it on purpose 🙄

[@TrimutiusToo]

Such a cliffhanger

[@3manthing]

32:40 And what?... That's it?

[@rodricrack1072]

xD

[@IISH4RKZzII]

u look like an anime sensei

[@drekkerscythe4723]

Nice beard

[@helo3827]

I bet no one will respond to this

[@particleonazock2246]

No, 2 minutes barely passed, and what do we have?

[@helo3827]

@@particleonazock2246 nothing

[@particleonazock2246]

@@helo3827 A reply

[@helo3827]

@@particleonazock2246 LMAO

[@priyansushekhar1269]

SIR , your beard doesn't look nice so kindly shave it, otherwise the integrals are fine..........

[@IISH4RKZzII]

no he is cool