Trigonometric Substitution - Example 3 / Part 2

Trigonometric Substitution in Calculus: A Step-by-Step Example

In this video, I explore a basic example of trigonometric substitution in calculus. Trigonometric substitution is a powerful technique used to simplify integrals, but it requires different substitutions based on the expression involved.
In this example note that we first have to complete the square on the expression that we will use the trigonometric substitution on.

🔍 What You’ll Learn:

The concept of trigonometric substitution and when to use it.

Different types of substitutions for various expressions.

How to label the right triangle from our initial substitution and its importance.

A complete example demonstrating the substitution process and integration.

Tips for handling tricky integrals that may require additional techniques after substitution.

This tutorial is perfect for students looking to deepen their understanding of integration techniques in calculus. By the end of this video, you'll be equipped to tackle trigonometric substitution problems with confidence.

Don’t forget to like, subscribe, and hit the notification bell for more math tutorials and calculus strategies!

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[dudemburg]

You are amazing! I went to a tutor and didn't get half as much down than I did watching your videos. All class I mindlessly write down what the professor is saying and have no idea what I am doing. Then I watch one of your videos and get the hour and a half lecture learned in 20 mins. Please don't ever go away. My final is tomorrow and I plan to pass just because of you :)

[patrickjmt]

glad you like my style : )
it is what i want i want to see when i am learning something new: start very basic, get more complicated!

[EduardoZ]

I was getting my A** handed to me by my math class, but your videos are truly helping me out. You don't know how much of a help you are to me right now. I have my 1st math Test tomorrow and I'm trying to cram everything in today! Thanks for all the work you put in to your videos. I know you hear this a lot but you honestly are a much better teacher than my professor. I didn't know how to do something so simple as the triangle because she confused me so much. You make it seem so easy!

[patrickjmt]

i agree. getting started is the hard part! once you know what to do, it is simply a matter of being careful with the algebra and calculus steps!

[arrowDnewt]

I think that a 1/(3^4) was dropped in the middle the previous video (part 1).  As I followed along, the (3/3) cancelled out when reducing the substituted trig function.  However, 3/(3^5) was the complete term, thereby dropping the 1/(3^4) term.  So the final solution should be multiplied by 1/(3^4) or 1/81.  

Please respond so I know whether or not I'm correct. 

I really appreciate the series on integration techniques that have been posted.  Thank you for taking the time to share your expertise.  

[MickeyMouseFan]

thnx so much!!!...my first year university calculus exam is today. so this video is my lefesaver right now...saved me hours of tryin to figure this out!

[patrickjmt]

@11m0 yep i did, pretty sure there are annotations about it

[Alain]

Patrick words fail me to express my thankfulness. This was confusing to me before, but after viewing your videos, it turns out to be clear to me. Thanks alot. By the is there a way you can be my tutor? If yes let me know.

[imCatiano]

thank you Patrick, you helped me alot in many math subjects.
plz keep going

[bozobarr]

I absolutely LOVE your videos! I probably owe you hundreds of dollars in tutoring fees.
I think your link from your site to this video is linked to Ex3 pt. 1 instead. YOU'RE my HERO! THANK YOU!

[mrandyinf]

because of your video i bee doing good in CAL II, I intentionally sleep in my math class because my professor so suck in explain this and he will make you so confuse if you try to pay attention, I do that because i know your video are great in explaining the concept. Thank you

[usamahkhan]

great video, this is really helping me with my class, thank so much. just one thing tho, just to let you know, the link on your website for this video actually goes to the first video i.e part 1. not that i couldnt manage find this video but i certainly did panic a little when the first one came up again. keep doing what you do!

[DLilsaint]

THankU soo much, appreciate u waking out of your bed.From understanding nothing toactually working out a question. What an accomplishment!

[Hemsomrojder]

Thank you so much for this! Ive been having problems with the last steps (the "backtracking"). I dont know why I didn't draw triangles. Makes it alot easier.

[blackphoenix]

:D Thank you so much for your awesome examples and work!!! I like the way you do you summation signs (I know its not on this video probably one of the intro to integral videos). I started to write my summation signs like that too because they were so awesome. Anyways you helped me ace Cal 1 part 1 final last term :D thank you!! Thank you for providing us with this really long trig substitution example as well.

[mandelblume]

It has been very helpfull specially this video!!!! I study physics and it's great that you can get some help here!!

[damnbdboy]

21, 000th viewer :)
Even though I have my college calculus teacher,
I consider you as my main math teacher.And Im ready for my quiz tomorrow.
- Thank you Patrick~!!
Happy Valentines day!

[cherryshin]

you are better than my calculus prof. thank you sir! :)

[patrickjmt]

@SirDroops great :) hope i can help you a bit

[itsmevan]

NOW I KNOW . THANK YOU PATRICK - EVEN - EVEN !!! RAWR