Trigonometric Integrals - Part 3 of 6

[gendrygaming]

Guess what! you are the reason why i pass my Calc I (Differential Calc)! and now im here, watching AGAIN with your videos hoping to pass my Calc II.

[mikeahmed]

You have helped thousands with calculus. All of us truly appreciate you taking the time out and making something complex as calculus easy for us. Thanks again

[patrickjmt]

glad you like my videos so much :) happy that they are working for you!

[ZSker]

I usually do notes in class and label them teacher notes then when i have the time at home I go to my laptop and start some notes labeled patrickJMT notes. I rarely use the teachers notes and I always use the notes I get from your YouTube channel. Thank you.

[SNPALLSNPRS]

I have a test tomorrow on all this stuff, I watched a few of your videos and went from a confidence level of 0 to a confidence level of 100, thank you so much!

[soseykat]

People should appreciate patrick.. Thank you God Bless you man

[bozardo]

You videos are so helpful! Usually, I look up all the lectures of the semester, and I make sure that whatever concept (let's just say "integral by parts") that I will go over that day, I watch your videos before hand. Thanks so much!!

[danielaiortiz-diaz]

I love how shorter videos are easier to watch till the end. Patrick you are the best

[TheGLD]

I can't thank you enough for your videos Patrick. My teacher makes everything so complicated and acts like it's so easy :( you on the other hand, make everything so simple! You're amazing

[Araaabmoney]

What's hilarious is that how our professor taught us how to do these integrals. The professor stated that it would simply take too much time to teach us through example, so in the middle of class the professor instructed us to "google", and go through our textbook for formulas in order to solve these. In essence, we simply used reduction formulas. The one example the professor did, they used a reduction formula as well. Tomorrow is my exam. We have to use trig. identities. Thanks a lot man!

[cxcatatonic]

THANK YOU SO MUCH for making videos! Thanks to you I will make it through Calc! You're amazing!!

[EatShanklish]

@patrickJMT I think what he means is to use the U- sub method before you distributed the sec^2 onto the (1+tan^2). So u=tanx, du= sec^2, so S (1+u^2)(du), then integrate to get U^3/3 then swtich it back to Tan^3/3.

[CowboysSB]

Thanks Patrick, your the type of people that make a real difference in the world. Great job mate.

[FeudOfJustice]

Patrick I just wanted to say how grateful I am that you've taken the time to do these videos. You have no idea how much help they've been over the last few years. (Almost done!) So once again thank you. Also you wouldn't happen to do anything with Statics or Physics by chance would you?

[MantraEdits]

In the second problem why does he distribute the secant squared to the 1 and tangent squared. Can't you just do a 'u' sub and let u equal tan?

[killazerg]

Great video. I just want to add something for some of you like me that like to make things easier:

Like the first case, the second case can use U sub earlier in the process, and IMO, becomes easier. Instead of splitting the integral, it is possible to make a U sub for tan(x) before distributing sec^2(x). You end up with (1+u^2)du, which equals the final answer PJMT got

[patrickjmt]

@hassancheetah you are probably right, i take the scenic route on a couple of problems!

[javirenpa]

Could you not have done a "u" substitution when it was, integral of (1+tan^2(x))(sec^2(x))dx? u= tanx, du= sec^2(x)?

[toddj.]

For second example, it's easier to let u=tanx, rather than distributing and breaking into 2 integrals.

[joshuaizquierdo]

dude I fucking love you, I have been up for hours trying to learn these problems, a few minutes watching your vids and I am ready for my final!!!