Improper Integral - Infinity in Upper and Lower Limits

[tckelly38]

Thank you so much PatrickJMT!

are you afraid to use tabular integration?

cheers!

[deyomash]

oh haha, sorry you just mentioned it yourself :)

[deyomash]

i'm confused, you start using t--> + infinity instead of t---> -infinity

[Milioo93]

Sorry but why is infinity divergent?

[patrickJMT]

@Milioo93 because it is not a finite number

[MathIsMyAchilles]

Hi Patrick,

Just wanted to say how incredibly useful your videos are, much more useful than any prof or textbook resource. Now, I know this is more than likely a dumb question, but I've fallen behind in calculus (university), and was wondering how can I catch up / what should I do? It's obviously a lot a material. To be answered would be an honour.

Thank you very much for your time

[patrickJMT]

@MathIsMyAchilles it is really impossible for me to say what you would need to do to catch up since i really have no idea about your situation. the best thing would be to speak to your prof!!

[SecantSquared]

hey patrick,

your videos are great, thanks for making them.

Is there any way to see the list of your tutorials organized by sub-subject or theme as opposed to the alphabetically ordered list on your website? (I know its already organized into Calculus, Discreet Math, etc, it would be easier to navigate consecutively through your videos if they were ordered by say...a section on integrals, a section on volume and surface area, etc)

Thanks!

[patrickJMT]

@SecantSquared well, the calculus stuff is all in order for the most part. the rest i am in the process of getting organized.

[LadySaberKnight]

I wish I were cool enough to do calculus in sharpies...

[Yousra730]

Can we integrate using by parts?

[quanta407]

I think I found my error, but you can still work the problem if you have time. You are an excellent teacher.

[quanta407]

can you please work integral x * e^(-2a*abs(x)) * dx limits - infinity to + infinity



[Sharpryno]

I know I cannot be the only one watching 30 of the these videos the day before the Calc2 final.

[Krazyarab69]

you should get a reward for being the worlds greatest teacher.

[patrickJMT]

@Krazyarab69 thank ya very much : )

[iamasuperbunny]

i love this guy. hope the feeling is mutual ;)

[patrickJMT]

@iamasuperbunny HUGS iamasuperbunny

[MultiMoe91]

i would turn gay for you patrick

thank you so much for the video :)

[PeeteZa]

I was at my University and for a second, I thought I heard your voice lmao, I freaked out and checked in the glass reflection on the classroom door from the hallway, I felt like I was going to see a celebrity haha

[arora7sid]

Won't your second interval go to negative infinite thus making it equal to 0?

[varuninnz]

you are a legend

[wildcaterick1992]

Great video!! I learned a lot however I will disagree that -1/3e^(-t^3) goes to infinity because isn't -1/3e^(-t^3) the same as -1/(3e^(t^3)) which means that you would have a number divided by infinity which equals 0. Which also means that we will need to do the other side you stopped at right? Thank you for the video it did help a lot!

[redbullion01]

@wildcaterick1992

I thought the same thing at first, but if you bring the e function down into the denominator then -infinity stays negative. Then when you plug in the decreasing values of t, the e function goes back up into the numerator. For example, think about 1/(e^-2). That is the same as e^2. Hope that makes sense.

[integraleric]

Thanks for this :-)

[aznpimp182]

Dude u need the problem wrong it is actually convergent ... The answer shud be - 1/3 not infinity

[10tigro]

hii Patrick! soo you don't do new limits of integration with u?

because I 've learned that if you do u-sub you have to have new limits of integration in terms of u so you don't go back to x

[romanceintherain]

the limit of -1/3* e^(-t^3) as t approaches infinity equals 0. 

[xTPTBx]

Will problems ever ask what an improper integral diverges to? You found out that the first integral (from -infinity to 0) diverges to +infinity, but what if the second integral (from 0 to +infinity) diverges to -infinity. Then you are left with +infinity+(-infinity) which is indeterminate...then what do you do? Or is that not even possible?

Thanks

[patrickJMT]

@xTPTBx if you bust up the integral, and one side diverges, then we say the whole integral diverges. it is possible for one side to go to +infinity while the other goes to -infinity. we still say divergent.

[tvoros17]

We love you Patrick!

[patrickJMT]

@tvoros17 thanks : )

[zoom2121]

Patrick JMT is taking over!!!

[xograchelle28]

this is so much better than reading my textbook.

[whytelyteCHOSENmc]

@xograchelle28 That's EXACTLY why I'm here. I was reading my text book and thought, "I HATE THIS!!!!" - YOUTUBE

[RedSecant]

question: what if you found like the first integral diverged to positive infinity and the second integral diverged to negative infinity. So it was like infinity - infinity. Does that ever happen??

[bfische2]

if you plug (-inf) into e^(-t^3), shouldn't it be 0?

Because e^(-t^3) is actually 1/e^(t^3). and 1/e^(-inf) is 1/(-inf), which is equal to 0. Am I wrong?

[RedSecant]

@bfische2 yeah. e^(-inf) = 0. Look at the graph of e^x. as x approaches negative infinity you get 0 so it's actually 1/0 which is infinity (but only because it's all a limit).

[lufcgalo]

quality videos

[Monsterenergy791]

Great explanation...not a surprise :-)

Keep up the great work!

[ARosstube]

I Appreciate the video

[sugar456789]

You're definitely making my calc 2 grade better. Thanks so much :D

[heroinkillz1]

Thank you! Super helpful!

[jonduncan2]

Question: If the first integrand diverges to -infinity, and the second integrand diverges to positive infinity, are we to apply L'Hopital's Rule somehow, since upon combining them, they neutralize each other? or choose different parameters in creating the two expressions?

Or do they still, somehow, diverge?

[mwbaseball90]

has anyone ever brought up the fact that you're left handed and really good at math which is processed in the left hemisphere of your brain...but the left side of the body is controlled by the right side of your brain? idk seems like there should be a relation there but I guess not

[xxilikemustardxx]

id love to know what all this was grrrrr

[patrickJMT]

@xxilikemustardxx grrrrr just some of the human race's crowning intellectual achievements

[DontComplain]

near the end. i don't get why when you plug an negative number into e ^ - ( t^3). it equals a positive number...?

[viper56610]

haha nevermind about my previous comment, I see you caught your error at 5:50

[viper56610]

At 4:10, shouldn't 't' be approaching negative infinite?

Thanks so much by the way, your videos are so helpful to me. I feel like I learn more from you then I do from my Calc 2 teacher!

[randyw8483]

@viper56610 That is what I was just thinking.

[sprinkleOFkawaii]

could u post some more improper integral probs? i saw all of them but i think just another hard prob or 2 would reinforce it better : ) please and thank u <3

[lusixoxo]

lol nvm ok i see the negative infinity sign..it actually make it positive.

[Sheepy5757]

great job man, thanks a lot. Keep em coming

[cwhatididthere]

:-D

[MunchVids2]

your vs look like square root symbols.

[dedemon111]

okay ignore my last comment cuz i continued watching the video and now i feel like a dumbass

great video though

thanks bud

[dedemon111]

Patrick when you solve the integral through integration by substitution and u replace the limit/the bounds i believe it should be limit as t--> -inf u have it written as t --> +inf

i may be missing something, but i just wanna make sure

[Weeeman5872]

When you split up the integral, would it have been okay to flip the limits of integration on the first part. As this would allow you to use the same variable (which shows it has no solution as they cancel out?)

[rak1212]

awesom possum!! thank you

[WaylonWillieNMe]

Patrick JMT taught me calc I, and now he is teaching me calc II. This guy is unstoppable!! I would be a calc noob without your videos, keep them coming!

[kureselhayat]

thanks bro , i appreaciate for your effort. It s gonna help me in exam today.

[krisjrosson]

Thanks man, you definitely gave me the light bulb above my head and broke my misunderstanding of this concept. Pretty easy now. Thanks a lot!

[andy120692]

oh man, I don't know what that Squiggly "S" thing is.. lol I guess I haven't gotten to this lesson yet

[myturtledaisy]

Its the integration symbol. You'll get to it after you learn derivatives. : )

[DrIntrebec]

your v's are awesome they look like square root symbols

[patrickJMT]

ha! someone i spoke to about 2 hours ago told me the same thing!!

[DrIntrebec]

hey patrick, check out my vids here in a couple weeks and/or days i know you'll love them cause it's math and i learned alot from you and math t.v. but your better cause you're WAY!!!!!!!! more funnier!!!!!!;)

[canadienne99]

thx a lot for these VDOs...good job =D

[gremlinextreme101]

Can the summation of two divergent integrals be finite?

[gremlinextreme101]

I mean, say the second part approached neg infinity then the sum should be zero, shouldnt it?

[MoroccoFriendofUSA]

Sorry Patrick but Grem is correct. The limit of the first part should be -1/3. Infinity is in the denominator, thus the limit equals 0 at your point.

[ashk1a]

tanx..soem thing like this question was in my exam..

[21chuck]

whats the point of setting up the limit if in the end were just going to plug in infinity like any other limit of integration?

[patrickJMT]

well, infinity is not a number, and it should not be treated like one

[21chuck]

your videos are excellent and cover all the topics I need, thanks for putting these up!

[patrickJMT]

hahah somehow i doubt that

[malicious6]

@patrickJMT Haha, thats funny, in order to get started on my homework, I just pull out one of these videos and it helps me ease into my homework. It sort of relaxes me too. As compared to a professor's lecture, its relaxing because if you miss something, you can just watch it over again.

[jacoblvmariah]

thank you so much for posting these videos they realy do help, thank you! ;)

[brilliantfranz]

Patrick you glasses rock, we all love them,

pretty nice explanation, as always.

Next week Ill be having an exam about integration methods and improper integrals.

btw what about if both limits existed and e.g. as you said it equals 1/2

Would that 1/2 represent some area?

[patrickJMT]

well, if the limits existed in both integrals, you would get two finite numbers, and combine them.

integration does not exactly tell you area unless both functions are positive...

[Syruscleat]

Dude, I may have made fun of your glasses which was improper, but you're right on the money when it comes to explaining mathematics. Bravo!

[patrickJMT]

my glasses rock!

and so does my background friend!

no one ever told me this was an academic setting. if so, i will make all the videos private and charge everyone tuition!