Improper Integral - More Complicated Example

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[@nicholasfazzolari3647]

Limits + Parts + L'Hospital's -- Gimmie layers of complexity. :)

[@dkblade27]

A little bit of advice... Please don't ever use the number 5 with variable s together. You're gonna confuse yourself, me, and others. Same thing with using the variable t. Not convenient with all the addition signs around.

[@mbcx4av316]

i agree i got into a complete mess with the 5 and s part

[@newarnav]

+dkblade27 z and 2

[@viewyourcomment]

t is the preferred substitution variable for the integral's bounds.

[@expiate87]

its not though. it can be literally any variable. preferred variable is a made up thing

[@viewyourcomment]

In most of the books you'll find it to be 't'. You'll find when you have more complex equations it helps to name variables consistently.

[@asemnafiz]

So this is what I do. I open a video of PatrickJMT, pause it, like it and then play it. Since I know that he is never going to disappoint me with what I am looking for and I am gonna like it anyways towards the end, I like it right at the beginning.

[@patrickjmt]

ha, very nice of you. but no person is an island as they say. i do not always have the answers, but i do the best i can!

[@asemnafiz]

patrickJMT You have influenced some people's lives more than you realize! You are the reason why I am still in engineering and have developed a keen interest in mathematics. I have learned a lot from you. I wish there was a better way to appreciate what you do other than clicking the like button. I hope you keep a backup of your videos. In case something happens to your KZbin channel, we would lose all these precious videos at once.

[@MovieTrim]

patrickJMT You do a really good job though. I passed cal I with an A- because of you. Now I'm watching these videos cause I'm in cal 2.

[@johnhampton9536]

+Nicolas Soto Your an ass clown bro.

[@thy7917]

+Nicolas Soto stop with being childish yourself, stop cussing.

[@AhmedAlhafid]

Definitely the best math instructor, i use your video to learn everything, well done sir

[@TrueLegend47]

I have a calculus test tomorrow. My teacher is Russian, has a terrible accent and handwriting, and writes faster than Usain Bolt on the race track, so I barely understood half of what she's teaching. You, sir, are my god damn Mathematics hero. If you were a teacher I'd attend every single one of your lectures and you'd be deserving every single penny of my tuition money. You fully prepared me for tomorrow. Thank you so much.

[@fggcreed]

Nooooo... was it Dr. K?? She kicked me out of her precal because I couldn't understand anything she was teaching haha.

[@alexyokiel4493]

I applaud you. You helped me tremendously in calc 1 and same thing with calc 2. You make everything seem so simple. Thanks so much!

[@patrickjmt]

hi bodacious! glad to help. if it makes you feel any better, this sort of video tutorials were also not available when i was a student. now, as a lecturer/tutor, that is why i make them!

[@biomerl]

This is the most evil math problem ever five e to the s five? s e to the five s?

[@patrickjmt]

ahhaha! i was 22 when i first started teaching at university - was even thinner and younger looking then. people did not think i was the one teaching the class! they thought i was a TA or something.

[@prosperousluck6063]

wow

[@MrLiveisevil]

I gotta say... patrickJMT you the best math prof i ever have... I am bad at these stuffs but because of u I managed to pass it all... with C's but I am happy...

[@yudhamica17]

I should just skip class and watch your videos and only go to school on exam days, because your explanation is much better than my teacher.

[@patrickjmt]

@PmQable1 absolutely my pleasure ; )

[@gunmetalspecter]

Hey patrick, just wanted to say thank you for all your videos. I took precalc and calculus over the summer sessions at my colllege during the span of about 10 weeks. Without some of your videos I don't think I would be in calc II now. And to top it off I'm still being helped along the way with videos like this.

[@patrickjmt]

@oOKrazyKOo yes, these problems can have lots of different things going on, so i thought it best to do one

[@Claugustus]

I have a quiz tomorrow thank you very much! How does it feel to have made a video 8 years ago that is still helping people today?

[@dontgotocollege5232]

Isaac Newton died 300 years ago

[@DarkLordAli95]

+Data Not Data LOL

[@taranjitkaur1854]

Well said.

[@whynot1322]

I have a test tomorrow, and I literally just went from 0-100 with the videos Patrick provides; I'm now confident in my skills, and actually am starting to like calculus ( weird ha!)

[@mutasworld]

Whos to say people wont be watching patrickJMT videos 292 years from now. hmmmmmm. HMMMMMMMMMMMMM.

[@Bodacious1966]

Patrick, I'm just beside myself with your videos thus far. I returned to school to get my engineering degree after a 25 year hiatus. This type of tutoring wasn't even a thought back then. I never had issues with math before, but when we got to improper integrals, I was stuck for some reason. I watched your video - sheesh nothing to it. Currently we are examining the various testing techniques for convergence. I just scrolled down your list, and they are all there. You are so great!

[@Jjsep91]

Thanks so much for the great explanations AND the beautiful handwriting! I've learned so much from your videos!

[@MetallicDETHmaiden]

"so........lotta." and cut

[@jfhowlpendragon]

Officially my idol. Really. You're amazing. I had so much trouble over this for ages and now it all makes sense! :D

[@DoctorLemonphd]

You are my hero. All of your videos have saved me time and time again in 12th grade calculus, and I thank you. If i ever win a major award for anything, I will be sure to mention you in my acceptance speech.

[@t.oguzunluerler4804]

you sir, are awesome. i mean really, really, really awesome. i mean your awesomeness diverges :P

[@1light4love]

😍 OOOOOOOOOOHHHHH that converged so well.

[@sarakitdotcom]

Thank you for your help, great explanation and step by step work!

[@fightingirishfan103]

Best free tutoring I've ever gotten.

[@Sergio-er1ez]

you teach way better than my calc 2 professor he didn't even mention limits which make it so much easier, thank you

[@patrickjmt]

@Digidices well, i do try. i get tons of comments and messages though so i can not respond to all of them!

[@PhotonCherades]

Pat you are getting me through 1st year calculus 10% above average and I am NOT a numbers person! Thank you keep it up.

[@chimera052491]

If i wasn't a college student without doe, I would donate to your website. Just know that you have helped me, are helping me...you're a hero in my book

[@JoanieAtwater]

Patrick is my hero... One thing to notice is that there's a pattern for these x^n*e^(-Ax) integrals. all you need if you see this on a test is this: n! / A^(n+1) Soooo in his example n=1 (the "s" raised to the first power) and A=5 (ignore the negative) plugging in his values: 1! / 5^(1+1) or 1/25 if this problem were: s^3*e^(-6s) then it's as easy as 3! / 6^(3+1) or 1/216

[@d1st1nct]

Excellent example to practice. Thanks sir.

[@rsadsultanov3071]

you are ace of aces/magnificent video thanks so much

[@Norpom]

I know I'm not "Patrick", but I figured I lend my thoughts regardless. My current teacher is sure to always tell us to "keep a clear mind." I know it's cliche, but it's very true. We're always worked up about how tough we think the problem will be, or maybe even by something not relevant to the problem at all. You know that you know the material, so just slow down, relax, take it step by step, and own it. Granted, this is easier said than done well, I tend to take too long on problems now...

[@ec515ss]

Thanx a ton. You saved me, I have a calc2 test in a week and i dont know shit. I just learned half of what I need for the test in like 15 videos. I'm going to use this all week, you're the best. (And you're about to have another 50 subscribers....at least)

[@erenkeskin6723]

You were so helpful man thanks!!!

[@Sylvanas590]

I echo this sentiment. My professor moves way too quickly. You're very clear and concise. Thank you for this video!

[@Wampa181st]

thanks a lot I always wacth your videos after I learn something in class

[@rorororororororox]

So helpful! Thank you so much!

[@camilanneo]

Thank you patrickJMT you saved my life!

[@FargandSirHomerlots]

THIS WAS SOOO MUCH HELP thank you. lol i havent really officially taken calc yet and this was really helpful for my summer assignment

[@MCTeacup]

haha I was doing the exact same question in my text book when I decided to youtube improper integrals... and you give an example of the exact same question! Got stuck on the infinity * 0 issue... forgot about L'Hopital's rule! Thanks a bunch.

[@faisalalharbi6971]

Thank u Patrick .. this was helpful

[@radiohead322]

aw YES. I was trying to do one exactly like this. and had no idea how to do it. THANKS.

[@shobhitrastogi9273]

I LOVE THE WAY YOU EXPLAIN EACH & EVERY TOPIC. CAN YOU PLEASE GIVE SOME MORE EXAMPLES OF COMPOUND & NON-LINEAR INEQUALITIES. I HOPE THAT YOU WILL HELP ME DEAR patrickJMT.

[@patrickjmt]

@buckeye2991 i just want you nice folks to be able to clearly see what i am writing :)

[@patrickjmt]

thanks!

[@patrickjmt]

@mangomann786 nope, although i have taught a good bit in my life

[@patrickjmt]

@rteyber i will try!

[@cracknigga]

i love you, man, thanks! this might even save my ass in the exam never thought about looking for answers on youtube though keep em coming, plz

[@MissMarissaaaa]

Wow, how perfect...I was doing this exact same problem and didn't even think about L'Hospitals. Thanks!

[@WrathofTim]

thank you for getting me through engineering

[@fosterp2004]

Patrick, first off your videos are awesome and thank you so much for doing this. I'm currently a calc 2 student and although I understand the material, I have trouble on tests sometimes because my teacher will combine several different techniques into one problem and I get overwhelmed. Do you have any tips on how to tackle these monster problems? Thanks!

[@jsgacol]

Thanks for the video, It helped me heaps to solve a similar exercise I had. Thanks for taking the time making them and uploading them. =-)

[@patrickjmt]

@alozonmo yes, cause things like history and art are just silly and worthless, right? whatever makes you feel good about yourself

[@patrickjmt]

@jw111892 price of education: going up. quality of education: going down (i'd wager). what a wonderful world: you get a larger debt with less skills to pay it off.

[@patrickjmt]

@missgina916 probably not

[@Jy-168]

U made my day bro, keep up you rock ^^

[@jeremy339]

Hey Patrick, can you please do a video on The Comparison Theorem. Thanks.

[@lncg10]

im so gonna send you a check when i get a professional job. Im pretty sure I've learned a lot more than what i've learned all semester from my professor.

[@reahslademhA]

i love u EVEN more for being left-handed. You're awesome :D

[@25suad]

Thank you dude!!!

[@eelnomtih]

Problems like these make me love math. They're so elegant! You've got integration by parts, the infamous zero/zero, the transcendent f(x) = e^x, and you solve a problem that asks a question about infinity... What more could you ask for? Totally cool.

[@jarpad1411]

I skip class to watch your videos and still get 90% +

[@DarkLordAli95]

im honestly considering doing the same exact thing... especially since my prof sticks with textbook exercises.

[@Tkdkid9]

@patrickJMT - Great review before beginning Laplace Transforms tomorrow!!

[@SarahKotb96]

I JUST LOVE YOUU!

[@integraleric]

I'll be sure to check out your channel. thanks.

[@Osiyor]

Patrick, i was wondering if you can make a video on the comparison test for improper integrals... am sure it could have been used for this particular problem... Thank you

[@patrickjmt]

@asaadalsabbagh happy to help

[@cuteNOBITA]

it is because, let say t = infinity, when u plug in infinity into e^5t, it'll yield a value that goes bigger and bigger or simply known as infinite. meanwhile, e^-5t can be written as 1/(e^5t) , when pluggin infinity, u divide 1 with a big number which will yield a value that is approximately close to 0. that's it :)

[@Nemception]

Thank you!!~

[@capabilites]

You must feel like a boss with all these love comments to you. Here is another one: you helped me so much, you're awesome! (Frames are available at Walmart for $5, I recommend Bradley hand Font for the quote)

[@patrickjmt]

just trying to make the internets a place to go for some math help!

[@patrickjmt]

@honeypot11 magical!

[@franknguyen007]

Can you do some vid on the comparison theorem for improper integrals ?

[@hypershadw]

A negative exponent is the same as a positive exponent on the bottom of the fraction. Notice that whenever it was on the bottom he had it positive and not negative. Hope that helps.

[@DivertimenticonKota]

Patrick JMT, You have helped me a lot inCalculus but I still have a concept that is not very clear, the Parametric equations. Can you post a video about ? Thank you very much.

[@CodyCleggMusic]

That was like... the best math problem I've ever seen.

[@patrickjmt]

@kareem0824 thanks for remembering me

[@Juxtaroberto]

Because you're undoing the chain rule. The derivative is the opposite of the integral, so when you integrate, you're trying to find the thing you took the derivative of in the first place. Because the derivative of the exponent comes down and gets multiplied, if you said your integral were -5se^-5s, take the derivative of that and you get something huge, because you need the product rule. You're trying to undo the chain rule, so you're anticipating the -5 that's going to come out, with the -1/5.

[@jayspenh]

thanks so much now i get it!

[@warotimi6182]

thanks so much for your videos. i guess i won't be needing any textbooks

[@Kheimp]

When you did L'Hospital's on t*e^(-5t) at 8:00, how did you know to place e^(-5t) on the bottom of the fraction? Would it have mattered if you had placed it on top? Also, I thought L'Hospital's was just to take the derivative of the top and bottom?

[@patrickjmt]

@Genocide1812 try watching a video on the topic before you go to class; i think you will find you get much more out of the lecture.

[@AJ-lf7gz]

I love you Patrickkkkk.

[@patrickjmt]

;)

[@ferheendumkagec2989]

thnq prateek...:-*

[@jjhump311]

I learn more in 10 minutes of your videos than I do from 75 minutes in class

[@patrickjmt]

@lilmizzheather91 i accept checks and cash.

[@wellitstrue102]

@7thbrah :O @patrickJMT you should definitely have done more from that book

[@OfficialAbednego]

tab method would work great here

[@rufinator007]

@aStrimbu agreed, but i would prefer a money transfer as well.. paypal?

[@honeypot11]

HAHA this was the exact problem that i got stuck on in the textbook before i went to look up your videos =D awesome online tutor indeed C:

[@electricfeel0]

I think you should change your name to Math God. THANK YOU so much for making all these videos!!!

[@patrickjmt]

@jwmcmac or is it HER?

[@Bodacious1966]

EXACTLY!!!

[@ryanwalker4491]

Come back to ACC Patrick I'd love to have a class with you! Your teaching techniques are out of this world :)

[@patrickjmt]

hahaahh thanks for the invite, but... nooooooooooooooooooooooooo way!

[@ryanwalker4491]

Hahaha well at least know that we love you here at ACC! I'd drive all around Austin from Georgetown if you came back :P I'm buying your book this Friday to help out with my Cal 2 class.

[@patrickjmt]

thanks for the kind words, i appreciate it. hopefully the book will help you out in the class!

[@walshy0001]

patrickJMT I may be completely off, but ACC as in Austin Community College......? UT Austin student checking in lol

[@ryanwalker4491]

walshy0001 Yup Austin Community College :) Good luck in Cal 2 bro. Finished with the happiest B of my life lol.

[@vaccarovj]

at 8:50 it should be "the derivative of t (with respect to t of course)is one"

[@NothingXMuch101]

hey y'al ... just another somewhat struggling calculus II student, if this was a U-sub problem. when expressing the answered integral with limits (assuming U-sub it's been used), Does the Upper bounds and Lower bounds of the integral needs to be evaluated with respect to F(u)??

[@beauburris7739]

I don't know if you went over it yet at the time time you made this video but you could've used tabular integration instead of separation by parts. It is a life saver for me in AP calc.

[@tuto09]

@patrickJMT Hey pat why didn't you use tabular integration to solve the integral of s*e^-5x. Isn't easier then doing a tedious integration by parts?

[@nicholasmaloof8378]

Did you omit the limits of integration when integrating by parts because they were 0 and t (and thus wouldn't really be necessary)?

[@mohamedbadawy6889]

I sware,not kidding, that you are better than my proffesor to the power infinity .

[@3z00z1]

@adreniln If u=-5s then du/-5=ds........where did u get the s at the end? the derivative of -5s is -5 only.