What Integration Technique Do I Use ? Example 2

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11 жыл бұрын

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! 30 Challenging Integrals with Detailed Solutions: www.teacherspayteachers.com/Pr...
What Integration Technique Do I Use ? Example 2. Determining how to integrate a particular function can be challenging. In this video, I try to show how I approach them.

Пікірлер: 104

@SepiaDragoonGR 5 жыл бұрын

This is legit the best horror movie i've ever watched. 10/10

@ozzman1997 8 жыл бұрын

Calculus: Where a solution can look more intimidating than the problem that you started with.

@seanki98 9 жыл бұрын

This deserves a standing ovation.

@patrickjmt 9 жыл бұрын

Clap clap

@DeadMeme5441 8 жыл бұрын

+patrickJMT lol Clap clap by us to thank YOU!

@Snoop_Doge 8 жыл бұрын

if our prof bring a question similar to this in a final or midterm, i will dance naked in the uni

@yootantonystark2738 6 жыл бұрын

so did you dance?

@syafiqadly9428 5 жыл бұрын

You have video of it? xD

@hamdimohammed2541 3 жыл бұрын

No worries, I'll join you! :P

@mattt1994 11 жыл бұрын

Just finished the last university math exam I will ever write. Thanks for all your help Patrick and best of luck to anyone still writing finals!

@freshely9309 5 жыл бұрын

This video single-handedly developed my understanding of integrals, calculus and trig substitution in one video and one equation! Thank you so much, I now know much more about the fundamentals.

@BurritoBalladBBd 10 жыл бұрын

Just wanted to mention that I had purchased the problems and they were extremely helpful for my Calc 2 skills. If you're struggling you should really consider it.

@dpcon1994 10 жыл бұрын

That is intense... fair play...

@jeevashanmugam7608 5 жыл бұрын

Your problem solving abilities are freakishly inspiring

@matthewmartel9295 7 жыл бұрын

I hope this isn't one of the questions in my test tomorrow...

@patrickjmt 11 жыл бұрын

i found calc 3 harder personally.

@tiisetsojames6378 10 жыл бұрын

Patrick you the man man

@dude157 11 жыл бұрын

For problems this complicated, i use wolfram alpha

@gotmilk606 6 жыл бұрын

What an epic journey this has been. I thank you.

@user-xi4xq9zz5w 7 жыл бұрын

you can use trig sub from the beginning and get sec^2(theta) ln(sec theta) and then use IBP's ,by differentiate ln(sec theta) and integrate sec^2 theta . I integrated tan^2 theta by rewrite as sin^2 theta/coc^2 theta ,, actually rewrite as sec^2 theta - 1 is way easier

@212ntruesdale 5 жыл бұрын

Excellent! However, I integrated tan^2theta by rewriting as sec^2theta -1, making two well-known, easy integrals.

@elbay2 11 жыл бұрын

Patrick, this was very well explained, and was quite the example! The only thing missing was partial fractions! Well done!

@georgesadler7830 4 ай бұрын

Thank you for the video.

@jegoodarms1559 9 жыл бұрын

I can understand him better than my own professor. Good job!!

@Survive2ToThrive 11 жыл бұрын

more more more examples like this please, loved it!

@willemjacobussnyder8596 6 жыл бұрын

Dude without this channel I would definitively have failed math this year. You're a legend bruv.

@feelingzhakkaas Жыл бұрын

Absolutely wonderful

@nonyvip1 11 жыл бұрын

I love your videos so much

@messi3119 9 жыл бұрын

first trigonometry.....after that hyperbola parabola ellipse and now...integrals!!! THANKS patrick :) before your tutorials maths for me a nightmare bt now i can easily solve all the problems....thanks once again

@alaaashraf8472 10 жыл бұрын

thank you very much it is very helpful. i am a student in cairo university of engineering and i love your videos thank you

@patrickjmt 11 жыл бұрын

i use my head

@willieklein6707 5 жыл бұрын

An absolute beast of problem!

@swagconundrum 6 жыл бұрын

You are an amazing human being

@gene546 11 жыл бұрын

man you're great, thanks for the videos.

@shiRo484 8 жыл бұрын

YOU"RE THE BEST!

@cjohn41 11 жыл бұрын

Jeez big pat... that was impressive

@elizamlokozi9833 3 жыл бұрын

thanks much for this program am a form six student having one month holiday but am able to study integration without a text book ,more integration questions please

@hamamath7195 11 жыл бұрын

thx man you are very good i love math for ever

@aleeexisss00 11 жыл бұрын

You are so awesome.

@lanolinetoring6097 5 жыл бұрын

Oh my god!!! Youre so good.! Thanks for the help man :)

@patrickjmt 5 жыл бұрын

you are most welcome!

@AnthonyMoody 5 жыл бұрын

1:22 I think you can start off with a trig substitution letting x = sec(theta) then using by parts after you get to sec^2(thet) * ln(sec(thet)). I got the same answer in the end so ..unless I made a convenient error 😂(which is definitely possible)

@jongeetard1259 11 жыл бұрын

@E.AmmarAmmar Switch the limits around, let s=0, you get -(-2 to s) 1/x dx, integrate, -ln |x|, insert the limits, use the logarithm rules to get ln |-2/s|,then ln(2/|s|) and evaluate the limit as s->0, which is infinity if I remember right. I think that's how you would do it. Please correct me if I'm totally wrong.

@mattt1994 11 жыл бұрын

Good luck!

@Hunar1997 8 жыл бұрын

if this was an exam i prefer leaving it and don't care about the marks

@omaralanis9436 8 жыл бұрын

I solved the problem myself before you showed your method, and I got the same answer doing trig-sub first and then IBP. Will that always work or was this just a lucky example? I got ∫[sec^2θ*ln(secθ)]dθ after my first step...

@ShyamSundarjps 8 жыл бұрын

You can use this rule to get u and dv... and its called [ILATE] - (inverse trigonometric, logarithmic, algebraic, trigonometric, and exponential) arrange the given integral in this order to get u and dv easily. u will be the first term and dv will be the second... :D

@stupid2574 6 жыл бұрын

I learned to switch the I and L so LIATE. Do you know which is the correct way?

@northernskies86 6 жыл бұрын

It's LIATE (you will see it spelled out this way in every calculus textbook.)

@Puxladen 3 жыл бұрын

thanks brooo

@patrickjmt 3 жыл бұрын

No problem

@thatoneguy257 10 жыл бұрын

how did you know to use sec for the U sub

@Engineer1T6 11 жыл бұрын

im pretty sure that Calc 2 covers all of integration, serieses, polar coordinates, vector valued functions calc 3 is surface integrals multiple integrals stokes theorem, greens theorem, partial derivatives

@carolinemitchell5711 8 жыл бұрын

The nightmare is over. Fantastic!

@majrohi1 11 жыл бұрын

Hey Patrick, Can we us the integration of (tan^2 X) as = ln(sec^2 X)+C.. Coz I know the integration of a tanX is indeed equal to ln(secX)+C. but not sure about that square of tangent.

@cdubbz11188 11 жыл бұрын

Any input on difficult wronskian diff Eq's?

@alexandretaranoff714 7 жыл бұрын

Just wondering why is dx = sec teta tan teta dx. Because i thought the derivate of sec teta = -1/ square root of 1-teta^2 right ?

@russiachan2 6 жыл бұрын

Just so you know, you can also use trig substitution at the very beginning and get the same answer.

@PARAMETATRONIC 7 жыл бұрын

Maany thanks Patrick! You are the WD40 of rusted brains :) Btw since tan is an odd function souldn't we consider the sign of x such that tan(theta) = (x/|x|) . sqrt(x²-1) ?

@king39355 11 жыл бұрын

could u solve this improper integral integral from 0 to -2 for 1/x

@MarkMcDaniel 6 жыл бұрын

Intregration domination!

@sunilagarwal712 6 жыл бұрын

Wow!!!

@rajanpoli4066 4 жыл бұрын

how u know u have to take x=sec theta ..i took x=sin theta .. and it was a complicated answer . could you help me ?

@dontbugmefool 11 жыл бұрын

What type of pen is that? Looks nice :3

@beta5770 11 жыл бұрын

nice problem

@xiii1818 9 жыл бұрын

Is this the only solution? it should be there's another way of the steps? Am I wrong?

@joe27941 11 жыл бұрын

I'm pretty sure you can actually instead start out with a trig sub, and then do integration by parts. That's what i did and ended up with the same answer

@cowpacino 11 жыл бұрын

this is off topic, but I love that rollerball pen, I have one just like it

@LifttheDead30 5 жыл бұрын

You could have used trig substitution right from the beginning, turned it into a basic integration by parts problem with u=lnsecx and v = integral of sec^2x.

@obo190 4 жыл бұрын

unffff

@codylaw7739 2 жыл бұрын

yes but then the ride wouldn't be as fun lol

@nubsmacker 11 жыл бұрын

For now I'm just a broke student, however, massive donation coming your way once I graduated! :)

@user-lm2kj9cn6j 8 жыл бұрын

this is ridiculous. I hope our prof doesn't give a problem as complicated as this on our finals XD XD.

@SNLshooter 11 жыл бұрын

What college did you attend?

@edderiofer 11 жыл бұрын

I saw the bottom part of the fraction and immediately thought "Aha! It's an arcosh integral!"... ...When I tried, I ended up having to work out the integral of x/SQRT((x^2)-1) anyway. Trust me to have overthought the problem.

@matthewk5827 10 жыл бұрын

Why couldn't you do trig sub for the first problem. x^2-a^2

@malishmodestopeter6017 7 жыл бұрын

I have got points , thanks but what does this statement mean "give three examples for Application of Integration"

@inertia9325 7 жыл бұрын

malish modesto Peter it means write down some places where you might use integration to solve something. For example, finding the area under a curve is an application of integration.

@broa948 8 жыл бұрын

You mean: if u don't know how to use trig identities... Just sit down and cry! hahaha

@mariahslittlelamb8049 5 жыл бұрын

idiot

@gddraftsman5617 9 жыл бұрын

why you uses sec teta

@tylerchengabc123 5 жыл бұрын

I know everything just watching the solution

@idknuttin 8 жыл бұрын

what kind of pen was he using?

@tommyommymmymyy 8 жыл бұрын

+idknuttin twas a pilot Precise. BEST PEN.

@prathedragon9847 6 жыл бұрын

Watch at 1.5x speed to save time!

@BLKro 11 жыл бұрын

It's a Pilot Precise V5 ;)

@jamesmoriaty1098 11 жыл бұрын

I'm only 3 yrs old n totally get this .... What most you tube commentssay to look smart

@alexthedude07 11 жыл бұрын

This demonstration makes me fear for calculus BC as I'm still in year 1...

@hamdimohammed2541 3 жыл бұрын

Integration is pretty weird and unpredictable, how on earth did arcsec end up in the solution? :| Also, is that the only solution?? Is the antiderivative unique? please reply, I wanna know