Integral Test for Series Example 1

[@UOttawaScotty]

Hey buddy, I actually agree 100% with what your saying here. I wasted my life pursuing all the vacuous things that society taught me to pursue, only to be left feeling empty and stupid. I cringe when the kids in my class ask why they need to know something...my new goal in life is to know as much as I can and spread that wide and far, I'm leaving my greedy lifestyle behind and focusing on things that are of social value now. The internet and people like Patrick are my saving grace.

[@theplasmatron3306]

me too dude

[@ChrisRedfieldFan503]

9:56 since the limit is convergence, then the original series divergence! who noticed?!! XD

[@Ez252x]

Haha, yeah he messed up. Since the integral DIVERGES the original series DIVERGES aswell.

[@qusaialkhu5261]

he corrected it at the end but unfortunately i stopped the video and went back to review that chapter again xq

[@janedoes5903]

Had to go to the comments. So glad I'm not stupid

[@CityofTreesFBL]

Throughout the video I was like "ok, easy. I got it. Feeling good with the steps" and then he said that line at the end I was like "welp, maybe I don't know it then. Let me pray that the comments think that what he said was wrong too"

[@emmyisamerican]

I haven't been able to endure a calculus lecture and I have a 95%... I owe you a lot of credit! Thank you so much! My highest grade and I'm an art student!

[@patrickjmt]

art and math go hand in hand; not sure why people think they are such separate disciplines :)

[@Paleopalescence]

to a new brighter tomorrow where education trumps decadence. We need to make education cool. When I returned to the US, I realized just how cool the smart kids at Uni were, people like you became my idols. I spent my youth wasting my youth and in my late 20s realized I had a job to do here, my job is to make education available to all by making it an integral part of pop culture.

[@cristian616]

I literally have not taken notes more than 3 times in class yet i've made 85+ on all my calc 2 tests after watching your videos.

[@ald3n3]

at 9:57 you said "since out improper integral CONVERGES then our series diverges." ... Did you mean to say "since out improper integral DIVERSGES then our series diverges."?

[@shumailahuddin2664]

He made a mistake. He meant the the integral DIVERGES, which in turn the series DIVERGES as well

[@Paleopalescence]

We need more people like you. Cool smart guys. There is hope yet!

[@hollandgraves1912]

"...the worst of both worlds..." haha you crack me up man. I watch these videos for humor as well as knowledge. lol

[@IluvHKong]

at 9:56 you mean the improper integral diverges?

[@MrM0hdhussain]

yes

[@aroojishaq1591]

THANKS MAN YOU ARE A LIFE SAVER! I have my calculus final for uni and this is helping me a lot!

[@Paleopalescence]

I was born in New Zealand to a Lithuanian mother and a half-Scottish/Half-German father. I've lived on every continent, I've been many different things and I have been through lots of ups and downs but yet all the while I thought about education and perfected my philosophy. We are not doing enough for our children. In fact, we are not doing enough for ourselves. Our culture is the culture of Sodom and Gomorrah! We need to change and social networking sites like this one are the way (cont)

[@hectorgarza3407]

Isn't taking the first derivative and seeing that its a negative number enough justification. I mean any number you plug in will give you a negative slope right?

[@patrickjmt]

you are very welcome!

[@saamiahmed7371]

Can we apply the Direct Comparison Test, for example n((n^2)+1) < n/n^2, which reduces to the p-series? Help please.

[@zeegh5867]

if the improper interval converges the series converges to but you said it diverges . so did you meant that the improper integration diverges instead of converges ?!!

[@TheCezv1]

zee Gh yes

[@1GENKILL4]

+zee Gh Yes I'm pretty sure he misspoke. The improper integral diverges, and thus, so does the series.

[@boing7771000]

+zee Gh Yes, he definitely misspoked. I also got stuck on the same point, but researched a bit to %100 to make sure and it should be said divergent no convergent, in the point that it approaches infinity.

[@spiritjustice9413]

CLEARLY POSITIVE

[@patrickjmt]

ha, no problem :) happy to help

[@dragonore2009]

A quick question, suppose you did have a denominator that could be factored that would make it undefined, would you still find the critical numbers in the numerator or is that if and only if you don't have a denominator that would be undefined?

[@aimeepadilla4109]

I know I'm late in all of this, but when you plug in the values at 8:52, shouldn't it be the natural log of 1 not 2? making the end 1/2 times infinity minus 0?

[@eiadessam1]

The function inside the natural log is x^2+1 not just x so he plugged 1 into that giving 1+1 = 2 hope this helps!

[@TurtleTakua]

Patrick, you are the greatest Sharpie ninja of all time. Thank you for saving my calc grade.

[@phorce88]

for finding if the the function is decreasing or not could you just say that since you know that the first derivative is negative and that the first derivative is the rate of change it is decreasing?

[@RaghuRamgvs]

In a general scenario, upon doing ratio test, if the function is independent of limit, what can we say about convergence? Comment on this plz!

[@alexchung2219]

the series is only convergent if the end result you get is a finite number greater than 0? what if it's a finite negative number?

[@ShadyToast]

Couldn't you use limits to prove that the function is decreasing? For example on the function you used could be shown to go to 0 after using L'Hopital's rule. Would that be considered adequate proof on an exam where u got about 5 minutes a problem? O.o

[@WorldOfDeepThought]

Doesn't the integral have to be from 2 to t after the U-substitution? (1^2+1)

[@Paleopalescence]

Hey, Patrick. Just wondering... when did you start doing this? I mean, when was your first math video uploaded to your channel? I hope that Salman Khan guy didn't steal your idea and become more famous for doing... a poorer job at explaining these complicated mathematical concepts to people. I think you deserve to be more famous than him because your explanations are just better. Also, would you mind if I posted some videos? Of course I would be posting stuff that you haven't (cont)

[@kevindarby8799]

If it goes to infinity it diverges, right? That's why the series diverges? That was just a hiccup? If not, im thoroughly confused...

[@baguduak]

+Kevin Darby you re right

[@spinseffing]

There's actually more to it than that. Many people feel this way with online videos. This guy is very good but if your teacher did this it would probably have the same effect. You're going out of your way and doing this on your own free time rather than being forced to sit in a class with distractions. These personal settings to help with the exact problem you were wondering about have been proven to be more useful.

[@thecottonjin]

Can you explain how you came to the conclusion that the improper integral converges when it = infinity? Doesn't convergence means the result is finite? thanks!

[@89TNash]

Already said this, but thank you again. Always a big help to have your videos. =)

[@GizmosShow]

Converges. The Test For Divergence is for the limit of the sum. This is the limit of the integral. Only diverges for - and + infinity.

[@TacticXerow]

Near the end he meant to say that since the improper integral diverges then the original series diverges too b/c an infinite number means divergence.

[@victornapoleonable]

I got quite confuse at the end, you seid "this improper integral converges, then the series obviously diverges" Please would you explain this tome. By the way how do I know if the integral result converges or diverges, let say values greater than cero means converge, and less than cero diverges.

[@mingzou6310]

hey Patrick, when you do the u-sub for the integral, dont we have to change the value of end point to respective of u?

[@hannahgomes]

+Ming Zou he substituted the value of u before substituting the limts of integration so therefore no so u basically have to resubstitute the value of u before the end points

[@hannahgomes]

+Giants115555 - Jared Jay there are two ways of doing it! You either change the value of the limits first or you can use the same value of the limits but substitute the value of the assumption before using the value of the limits.

[@hannahgomes]

+Giants115555 - Jared Jay you shld probably watch his basic integral video for better explaination

[@VvkV94]

It would be so much better is all the professors were mandated to get a teaching degree....thank you for the noble work

[@jacquibrzuchalski7341]

could you use l'hopital's rule for the infinite over infinite instead of the 1st derivative test?

[@r3g4rds]

Dont you do the derivative test to see where the series has turning points and therefore where it will be decreasing/increasing as x-> infinity?

[@whatshouldmenamebe]

decreasing on just the interval ya?

[@stephenmoore9040]

Thanks Patrick.

[@Reggie548]

I have done the derivative multiple times, I am not in fact understanding how your end product is that. You have a 2x and an x on top, they can't disappear with any form or property of mathematics.

[@TheTheone12360]

getting A's on my math exams since july :D. thank you

[@eric29292]

I found a complex root that makes the denominator zero, is this something I have to worry about?

[@lyyongan]

thank for your video. great help for me

[@indiewizard9458]

Why do we have to look first if the function is decreasing?

[@hannahgomes]

+emırhan celıkel because you can only use the integral test if those three conditions satisfy

[@chanothebest]

does the sum of x^(-0.5) converge from 1 to infinite

[@danideboe]

No it's a p-series with p

[@BluedvdMaster]

doesnt the improper integral diverge?

[@learndailyphysics4804]

thanks

[@MrBlash93]

Perfect. Thx u so much

[@alvingeorge123345]

i wish you could take my exams

[@cathyphilip7315]

Patrick you are my Heaven sent I love you

[@Paleopalescence]

posted yet like adding fractions or abstract algebra!

[@manuelaidos]

you can factor out .... you just go with complex numbers you know that square root of -1 is equal to i

[@danagamer]

I noticed that too!

[@ajeshav4322]

true

[@justicemike1014]

I love dis

[@valdez343]

no because the derivative of acrtan(x) is 1/(x^2+1) and so you'd be missing the x in the numerator.

[@brianvanbeek2083]

Mathematics is not a book confined within a cover and bound between brazen clasps, whose contents it needs only patience to ransack; it is not a mine, whose treasures may take long to reduce into possession, but which fill only a limited number of veins and lodes; it is not a soil, whose fertility can be exhausted by the yield of successive harvests; it is not a continent or an ocean, whose area can be mapped out and its contour defined: it is limitless as that space which it finds too narrow for its aspirations; its possibilities are as infinite as the worlds which are forever crowding in and multiplying upon the astronomer's gaze; it is as incapable of being restricted within assigned boundaries or being reduced to definitions of permanent validity, as the consciousness of life, which seems to slumber in each monad, in every atom of matter, in each leaf and bud cell, and is forever ready to burst forth into new forms of vegetable and animal existence. - James Joseph Sylvester

[@thomasr1072]

absolutely love your videos youre awesome but a small nuance in mic volume level video to video

[@aiicwyt6768]

Shoutout to Mr. Achille’s class!

[@mncedisithabethe1547]

Genius

[@MagicTsukai]

ty =]

[@yousorooo]

The improper integral is divergent but you said it's convergent...

[@DJDelta0]

Everything is so clear now...

[@atheeralmousa2432]

Omg i can’t believe i’m still watching this

[@airmanfair]

Continvos.

[@moesulieman7585]

anyone can help me to find integral ((a*x^a)/(1-x^a))^(1/ab)

[@kaktor31]

8.20 gotta be tan^-1 i guess not ln

[@linnguyen753]

hola

[@SuperAmizy]

i guess ur professor is the same as mine ur message is like 9 months old and i guess u dont have that professor any more as he decided to teach my year :P

[@Grandbox1992]

the improper integral is divergent!!

[@Sirsantos]

You Should be my GSI...

[@المقبالي-ل2ف]

from oman: thank you

[@sumeldhanoa2059]

LCT is easier in this case

[@thecottonjin]

oh. I see. thanks :)

[@cara9859]

watch on 1.25 speed if its too slow

[@alaazeidan7844]

Guys the integral diverges :)

[@DigitalChaoS]

So basically a nightmare.

[@StillTryingMyBest]

He mispoke, Just listen a few seconds after that he corrects himself unknowingly

[@moesulieman7585]

vvv

[@oxm18]

Does Patrick JMT have a PhD in math!!

[@patrickjmt]

Nope

[@Jfresh55]

+patrickJMT what kind of degree do you have? did you go to college?

[@Jfresh55]

+patrickJMT what kind of degree do you have? did you go to college?

[@topsecret6970]

i noticed i think he wrote the wrong thing in his last video

[@Ch3koElric]

Dude I love your videos and i find them VERY helpfull. However, the *tick* thing you do with your mouth is annoying.