Trigonometric Substitution - Example 3 / Part 1

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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[JulesManson]

At 6:10 you made an error. You factored out a 3 from the radical in the denominator but forgot to raise it to the 5th power after writing it to the left side of the integral..

[jamiekincaid]

Hello Patrick,

I have been watching your videos for my whole junior year. I have had the worst calculus professor that does not explain anything and just goes right into the problem never telling us his process. Your videos have literally gotten me through the math for my biochemistry major and I seriously do not think I would have made it this far without the help of all your videos. So I just wanted to give you a huge shout out and a ginormous thank you for all actual lectures you give, and for the number of quick tips and things I have remebered because of your videos. Do not ever stop making them please!! You are the bomb!!!!

[glisianator]

Hey man, your videos are super helpful when I miss my calc2 lecture. Really appreciate it.

[larmisdor]

at 6:17 isn't the 3 you factored affected by the 5 exponential? after canceling it should be 1/(3^4) not 1

[abuabdullah]

LOL I don't go to lectures anymore. Who needs it when you got Patrick!

[shoobyman]

Wow Patrick, thank you so much for this. I just had my calculus final exam today and got a question like this and your video came to mind right away.
It's because of this video that i did not forget to raise the factor ^5 when i was taking it out =)

Thanks so much man, you helped me a lot this year!

[norhussien]

dude tnx 4 the video... i hope it can help me for my exam tomorrow...tnx a lot...

[MrTuberViewer]

Hey Patrick, first off I want to say thank you. Most people can't explain these things as organized as you do. Second I'm just curious if you've ever considered using hyperbolic substitutions like cosh on sinh rather than tan or sec. My teacher taught it this semester and I think its incredibly useful. The derivatives are easier to work with and the properties are easy to remember. *cosh - sinh = 1

[epiplayer]

who would dislike this? very good video Patrick...makes calculus so much simpler

[Ktangsy]

You are the man! Your videos are very helpful and clear! Keep up the good work!

[deco]

i love you right now .... making my life so much simpler

[filipina]

@dustfinger91
im on that same boat right now in my summer 6 wk class :o. ive learned so much more from @patrickJMT in hours of youtube than lecture with my professor in 6 wks.

[WMDAEGZ]

I DON'T KNOW WHAT IT IS BUT YOU GOT IT thanks patrick

[jhonbus]

Anyone else get a huge sense of relief at 3:34?

[patrickjmt]

thanks! i will fix it... eventually : )

[patrickjmt]

@wilversweb i have annotations pointing out the mistake. thanks though!

[Sergio]

Hi Patrick. I'm believe you made a slight mistake in your calculation when you factor out the 9 from the radical. Before factoring, you have:

((9-(3sin0)^2)^(1/2))^5

So after factoring, you should have:
((9(1-sin^20))^1/2)^5

Which should then be:
(3(cos^20)^1/2)^5

Which is then:
3^5((cos^20)^1/2)^5

Which should then leave 1/3^4 outside the integral, instead of 1.

Do correct me if I'm wrong, however. :)

[Kavfall]

so the final answer should have everything into 1/81 or 3/243??

[Amvalson]

@TheEspritBelle I think you are right because I tried it too and I got the same answer as you. I think he just forgot to do 3^5. But the steps are really helpful.

[personaltip]

Hi Patric! Thanks for your videos! They are really, really helpful to me. I just have one question. After you took the square roote of 9, which is 3, I think you need to raise it to power of 5 befor you move it out of bracket. Because the whole denominator is riased to the power of 5! ie 3^5. Could you explain that part please. Thanks a lot for these videos you helped a lot.