Calculus 2 Lecture 7.1: Integration By Parts

Calculus 2 Lecture 7.1: Integration By Parts

[lordosmosisx]

This is exactly how calculus professors should be. They shouldn't be as dickish as they are just because a student doesn't understand the material. Some of us aren't configured to just "get it." Professor Leonard is excellent. He breaks things down and explains along the way. You can tell he cares about his students, and has fun along the way, seen in his comic relief. The fact that he is able to make students smile in a class as difficult as this shows a lot. You are a good person. Thank you for all your help!

[instaminox]

you should teach teachers how to teach

[gotosleep]

Professor Leonard- "I need to make sure that you understand"
My Professor-" If you don't understand go home and practice"

[DeeRandhawa]

Prof. Leonard: "Show of hands if you are ok with that one"
Me: Actually raising my hand with a smile on my face :D

[darthboganis]

Before, you made it fit the integration tables. IBP is the product rule for Integrals. 0:00
Deriving the IBP formula 1:00
Why Integration by Parts? 8:00
Choosing u and dv w/ example 10:30
Example 18:00
Process: Is it in the table(can you rewrite it)? Can you substitute? Integration by Parts?
> If it's not solvable.. consider IBP a second time on right side of plus sign, or substitution
Example 28:30 [Substitution or IBP?]
> 36:30 IBP twice
More examples/philosophy of IBP 41:50
What to do when IBP runs on a cycle? 52:00 add the repeating component (the component you are trying to solve for from the beginning shows up on the RHS) to both sides. This works because you have an equation effectively.
Example 58:40 integral of ln (x) w/bounds [1 to e]
Example 1:06:30 If nothing is working, break into components that you know you can integrate
> insert an identity to make it easier to solve 1:11:30
> sec^3(x) integral 1:16:00
> this problem also took advantage of repeating integrals which can be cancelled out
Reduction formula 1:29:15
Reminder on IBP philosophy 1:32:30
> using an identity 1:39:50
> splitting up the integrals, moving repeat component to LHS 1:43:00
> the official reduction formula for sin 1:47:15

[adame]

a little tip: If you ever want to know what to set U equal to in the equation use LIPET.
L is log functions (ln),
I is inverse trig (sin^-1(x)),
P is polynomials (x, x^2, etc),
E is exponential (e^x),
T is trigonmic functions (sin, cos, etc)

Do this in order, if you have int(xlnx)dx for instance, you set U=LN because it comes before polynomials in the pneumonic

This will work in any situation using integration by parts!

[riaregi]

I don't even know why I bother going to my Calc class because I learn more from sitting at home and watching these lectures. Thank you, Professor Leonard! Heads up to anyone reading the comments, but an easy way to pick your U is to follow LIATE (log, inverse trig functions, algebraic terms, trig, and exponential). It works most of the time so keep that in mind.

[Shadowbrothe]

Professor Leonard, I hope you get to read this, I started college 20 years ago, had a son in my first year, "took a break" to enter the work force to provide for my family. While I have done very well for myself without completing college, becoming a widely sought after industry leader in my profession, I decided it was time to continue my education. Fast forward 20 years I am working full time in a pretty demanding industry with quite a lot of responsibility and I'm trying to continue my education. Disregarding what I've spent in tuition for formal education, you are the reason I got an A+ in Calculus 1 (don't forget I've been 20 years out of school and only remembered basic college algebra), and now you are the reason I'm understanding Calculus 2. I can't express enough how amazing you are as a professor, and I will be contributing your Patreon. I've spent weeks and weeks trying to understand Cal1/2 from the book, and course material, and visiting a few of your lectures makes everything click into place. I can't contribute enough to your Patreon to let you know just how much you have done for me. I completed Cal1 with an A+ in 5 weeks after not doing advanced math for 20 years, if that does not speak to your ability as a Professor I don't know what can. I could only wish I had you as a Professor in person... Thank you!

[blakehill]

One of the ways my calc 2 teacher said to help remember the integration by parts formula is "ultra-violet voo doo"
UV - Int(vdu)

[victorotieno]

anyone who hates maths will change his attitude after watching your video...you are such a wonderful instructor....kudos

[tychothorpe]

It is an honor being taught Calculus by Clark Kent...

[DanT-iuoc]

was having a bad day struggling with Math and Prof Leonard completely cleared up misunderstandings. This man is a NATIONAL HERO.

[thebassofmontecristo]

Any Calc teacher would be hard pressed to come up with a clearer, simpler, better explanation than this one. This guy is a math rock star and has given me the hope of passing Calc2 with a high grade.

[FakeWonder]

If my whole class knew about this channel I'm pretty sure my professor would be without a job

[dementedfairy]

You lectures have actually allowed me to watch your lecture in my room when I'm too depressed to go to class. I must thank you for this.

[mastovlox]

For anyone else who's looking, Reduction Formula 1:29:40

[merritt]

You can pinpoint the exact moment that Professor Leonard's soul died when his students told him integral ln(x) equals 1/x lmao.

[MashrufKabir]

" Whatever you see, it goes for your V. "

- Professor Leonard

[vikesboy]

I can't say it with enough conviction, but YOU ROCK!!! There are EXPERTS who TRY to teach. There are TEACHERS who are not EXPERTS and then there are the type like professor Leonard: TEACHERS who are EXPERTS. Thank you!!

[mugdha]

All i've to say is he's a magician. Calc2 has never been better!Thanks prof