❖ Trigonometric Integrals - Odd Powers of Sine And/Or Cosine ❖

Trigonometric Integrals: Solving Trigonometric Products with Odd Powers

Description:

In this video, we explore solving trigonometric integrals involving products of sine and cosine functions raised to positive integer powers, where at least one power is odd. When faced with such integrals, the key strategy is to separate an odd factor and rewrite the remaining portion using trigonometric identities. This allows us to apply a u-substitution, transforming the integral into a more manageable form. We'll walk through the process step by step, ensuring clarity in how to approach these typical problems involving trigonometric products. Perfect for anyone studying integration techniques in calculus!

What You Will Learn:

Understanding how to handle integrals with trigonometric functions.

Applying trigonometric identities to rewrite products of sine and cosine.

Using u-substitution to simplify and evaluate integrals involving odd powers of trigonometric functions.

Key insights on how to recognize different cases based on the types and powers of trigonometric functions involved.

Patreon for extra math resources:

#Calculus #TrigonometricIntegrals #Trigonometry #IntegralCalculus #MathHelp #IntegrationTechniques #uSubstitution #SineAndCosine #PatrickJMT #Mathematics #MathEducation

[Tuanski]

You're the best math teacher on YouTube

[patrickjmt]

@ronniemonnie they will be equivalent answers; you can use trig identities to switch from one solution to the other! so, do not worry about it!

[laker]

@ Patrick, When I first changed to an Economics major last year I didnt know if I could climb the huge mountain of math. I took 6 classes in a year, starting from elementary algebra to calculus 1, I am now taking calculus 2 and I could say that with your help I have been able to ace my classes. I can now face the subject which I have feared for years and hold my head up high! Thank you for all of your help!! U rock!! Ur helping people overcome their fear of math!!

[Lulrage]

Thank you so much for making these videos. I've had the same Cal I and II teacher the past two semesters and he is a very good teacher he just likes to spend a lot of time explaining the theorems and proving them and it leaves very little time to see examples being done. Your videos are always a huge help to come look back on after class.

[Icecube]

just want to add that when you do trig integrals, you will run into problems that have more than one answer. some people might get confused if the book has a different answer. it all depends on which you choose to break up.

like for the second problem in the video, you will get a different answer if you chose to bust up sin instead of the cos. the answer is still right, but different.

[badriaibrahim]

Hello there sir patrick

I want to say

Thank you like alot

I just don't know how to say thank you in a good way

You are the reason why i got 96% in maths exam with knowing that i never understood from my teacher

Thank you very very much

[ccasek]

Hey Patrick, just wanna say thank you for all of the help you've given me. I watch the full ad now before every video. You've saved my calc grades.

[MVPSuns]

@patrickJMT
Thanks man. People really don't understand that students have to pay big bucks to learn the same stuff you teach you gift to the world. I just wanna say i appreciate it.

[patrickjmt]

glad it helps... i plan on working through a BC test at some point soon!! maybe starting today!

[crazylazy]

God bless you patrickJMT.
Helping calculus students one video at a time.

[TDProductions]

Been watching your videos for years. You literally have videos for every subject I've needed help with, ily.

[patrickjmt]

@solution91 nice to know that i have been helping you out for that long : )

[elwoodrock]

This is the best channel on YouTube. You make these problems look so easy.
Thank you!

[Wariowaftfart]

Who would have thought youtube is capable of teaching rather than distracting. God bless you and your videos.

[MrJPawelHeaven]

that's amazing how much somebody is able to learn by watching your lectures - thank you very much

[Yeppy]

I just want to thank you so much. Seriously all your videos are so helpful especially to a high school student that's trying to do their best in this class. You are the best!

[VIKT]

JMT, I love you, but some of your audio on your old videos drive me crazy.

[marcopetri]

Thank you a lot for doing these videos! I'm studying at Milan's Polytechnic in Italy, in months of lessons they didn't explane as well as you do how to do these trigonometric integrals. These are the reason that make me think about go abroad and never come back here.

[patrickjmt]

@viktorgoa congrats, that is very good!

[patrickjmt]

@Pocket2011 well, you can do a u-sub with u=3x and then proceed as normal