❖ Trigonometric Substitution ❖

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.
🔍 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!
#TrigonometricSubstitution #Calculus #MathTutorial #Integration #EducationalVideo #MathHelp #ProblemSolving #RightTriangle #IntegrationTechniques #AdvancedCalculus

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@zloyhimik typically people do not want to see it this way; using the right triangle produces a much more simple equation

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If khan Academy confuses you, then you probably have a below average IQ. How do u not understand that man? smh

[@mfm77x38]

trig substitutions are derived from the right triangle, and in the right triangle if theta is one of the angles then in cosine theta 0

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[@patrickjmt]

glad i could help :)

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Even though I have a great calculus teacher I love going to you for your videos. They help solidify the concepts and sometimes help me wrap my head around some concepts. Thank you.

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What I meant is, the steps just going through the problem is a lot. Thanks for your tutorial. YOU ARE A GENIUS.

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and? is that a long time?

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Needed this to refresh my memory. Taking differential equations next semester and need to re learn integration techniques.

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i hope the final went well!

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The hero that nobody asked for but everyone needed.

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As someone who stupidly decided to take Calc 2 online because he knew he'd be working nights and days (on different days each). You have saved my grades. Trying to read my professors notes he posts online, or follow his messed up organizational system is beyond impossible. I'd rather try to do calc 2, while still in middle school then try to follow some of his trains of thought. Whenever I get stuck I come to your videos. (Which has been a lot, especially for trig integrals). Only thing I wish you did more videos on, (maybe it's because it baffles me a bit) is when using washer and shell, I just would have liked more examples. That's it otherwise you are awesome!

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Thank you teacher! :)

[@patrickjmt]

You are very welcome!

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[@Jason-tc8vi]

Missed class when my professor went over this and you helped me get caught up. Thank you for posting

[@patrickjmt]

+Jason McCoid my pleasure! I ha e quite a few of these if you need more

[@Jason-tc8vi]

That would be awesome if you could provide links. I'm having trouble with the trig substitution when using x=tan(theta), dx=sec^2(theta)d(theta)... for example, integrate xsqrt(1+x^2)dx. I get the answer: (sec^3(theta))/3) + C, but I'm inclined, since sec = 1/cos, and i found cos to be simply 1, to use 1^3 and can't find any use for the hypotenuse of the triangle where ? = sqrt(x^2 + 1)

[@Jason-tc8vi]

Nevermind, dumb pre-cal mistake haha. You showed me what I was doing wrong in your next video. Thanks again

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@mirzconsulting i did once a long time ago and it was a terrible experience

[@AvengedRocker92]

Nice Job, Really helped me out with my classwork, and found some new methods of substitution Thankx!

[@patrickjmt]

there is a ton of stuff missing from my website. it is a nightmare to keep updated

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Thank you so much for posting this! I just learned more in 15 minuted from your video than I have in 2 hours of my calc class!!!!!!

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This guy is my favorite math tutor lol. Well done, great video.

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I have a quiz tomorrow on this hoping it will help.... I watch your other videos and UR DEF THE BEST TEACHER/WEBSITE ONLINE!! Id say better than KHAN ACADEMY! :D Thanks for putting this up you're seriously the best!

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Have my Cal 2 final tomorrow. Been binging these videos

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good luck!

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lol finally clarified what i was confused about in the last step…THANK YOU !

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started learning this topic this week, goes on this channel to watch a ton of examples and understand, you are the cod(call of duty) god of calc!

[@patrickjmt]

@pabloMTv ha, nice to see i am missed. i was actually spending some time getting things organized (playlists and stuff) and also working on trying to get some iphone apps out (almost there!). so, i have been doing stuff, just not creating new videos, which is unfortunate, as i hate organizing and like making videos. c'est la vie though, it is stuff that needs to get done! hope you are doing well!!

[@patrickjmt]

@angelsword1000 you are very welcome

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I could never understand my Calc BC class without your help, thank you soo much!

[@mrmoonmini]

really inspiring using substitution by trig it helped me a lot in integration topic

[@cgsuperpanda1]

Going from theta to x is what used to throw me off. I didn't know where to get all my substitution from. One of my friends tried explaining the triangle thing but he used it from the start and that only worked sometimes. D: So now I know: x to theta: memorize the rules/substitutions theta to x: draw the triangle. Thank you!! :D

[@patrickjmt]

@sunnysideup no problem, happy to help :)

[@patrickjmt]

@cgsuperpanda1 no problem, happy to help : )

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I wish my professors would teach at the same rate as you do :( they all go way too fast. Your videos always helps, I am very thankful Patrick!

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WOW that this video was so helpful. I missed lecture for this topic and after watching the video don't feel behind at all! You ROCK! :)

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i never understood the right triangle part until your video,thank you!

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I got it all up to where you have to put theta back into x before watching this video. Now I understand! thanks!

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thank you sooooooo much!!!! i had nooo idea how to figure out where the units go on the triangle... my professor always did it as one of the first steps and i was like huh? but doing it later in the problem like you did is sooo much easier to understand! thanks bunches

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You sir are a king.

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Wow. How convenient. I was just getting ready for a trig sub lab, and this video helped me out big time. You are basically my calc professor

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Dude how come you are so Smart? After i finish a course i usually forget most of the material but you are on point.

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@42marthacu glad you like them : )

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Holy hell.. this type of problem has it all.. a true test of one's mathematical prowess.

[@powercrazy11]

Can't understand a word that my TA says so this video definitely helped, thanks patrick.

[@Puggalug]

This example actually doesn't necessarily need trigonometric substitution. If you take an x from the x^3 and put it next to the dx (which would make the numerator x^2), you can then use u-substitution. Let u = 16 - x^2, x^2 = 16 - u, which means 2x dx = (-1) du, or x dx = (-1/2) du. You can then replace the numerator with (16 - u), the denominator with sqrt(u), and the dx with (-1/2) du, and it then becomes the matter of using the reverse power rule after some algebraic manipulation.

[@rt36crazyfists]

I was going to study all my notes and textbook for my final but I think I'll just watch your videos!

[@1213JayStar]

11:25 if you don't see the radical that you were originally solving for in the triangle, you did something wrong. However, you don't necessarily need to see the radical sign, but the radical you solve for should be in the original problem somewhere.

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Oh God thankyou! Im from Philippines. This really helps a lot specially now with online class

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Thank you! for some reason I could not wrap my head around this. but you cleared it up!

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Bruh watching you video was so helpful. I instantly figured out the trick.

[@mattsheehan7285]

thanks for making this topic easy to understand, keep it up Patrick.