Trigonometric Substitution 

Full 1 Hour 10 Minute Video: www.patreon.com/MathScienceTutor Direct Link to The Full Video: www.bit.ly/3zuP2s0

integration used to be so much simpler ... and then this came along

Trig sub is one of the hardest integration techniques to learn and you explain it in such an easy to follow way.

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2:38 "now we gotta do some math" legendary

I wish this channel had been around when I was in undergrad. I remember watching my professor explain this and wondering why this class was a requirement for Econ at UCLA. Now, many years later, I’m still waiting for a chance to show off my trig substitution skills. I’m getting my MBA in 2 weeks and I didn’t need it there either.

This is what online math classes should be like

For all you people struggling through Calc 2 right now, just keep at it and take comfort in the fact that Calc 3 and Differential Equations won’t be nearly as bad. I’m in D.E right now and it’s actually kind of fun!

When it comes to finding the missing side of the right triangle, it's worth noting that it always turns out to be the square root from the original integral that made us need to do a trig sub in the first place

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I watched this video an hour before my test in desperate need of help since I did not understand it. I saw a question and I got it right because of you. Thank you so much!

Love this guy but at 3:30 he dropped the square of sin in the denominator of the integral. Just for people that are trying to follow along

The last time I learned Calculus was almost 20 years ago, and this year I need to tutor Calculus. Your videos really really helped me. You are really gifted with being able to explain complex things in simple ways. THANK YOU.

I watched an hour long lecture from my professor and did not understand this but watched 2 minutes of your video and I already understand it better. Thank you for your service to confused college students.

damn-can't get away without knowing my Trig anymore. Looks like I have to do a whole relearning!

I would just like to say thank you to the organic chemistry tutor! You are the greatest! His videos have helped me with bio, chem, calc 1 and 2, and physics

I tutor calculus students and yesterday I realized I was rusty on trig substitution. This video was just what I needed; thanks for sharing!

This dude is covering calc2 while I'm doing it. It's one of the best feeling in the world.

🏃🏻‍♀️5 hours till my exam, i am grateful that u uploaded this today , thankkkk uuu

I’m so thankful you made a video on this, I went crazy trying to understand this when the textbook just put it with no explanations

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Revisiting this for calc 3. Thanks so much for your videos! They help A TON.

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This is by all means the hardest shit I have ever studied it!

1:12 Full list of trig formats & associated x=a formulas. Problem 1 (1:18-8:45); Problem 2 (9:02-19:24)

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For the last one, why can’t you do 9sec^3(arctan(x/3)) - 27sec(arctan(x/3)) + C?

This came out at the right time, I have an exam about this tomorrow, thanks

This chapter right here, is the core difficulty of all embodiment of Calculus holy shit

Helpful content as such shouldn't be locked behind a paywall.

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8:03 whoa! Much simpler method to determin tan(arcsin(x/2)), cos(arcsin(x/2)) etc. Until now I have used trigonometric relations and calculus to determin those functions.

This helped me so much with my Cal2 homework! Keep it up man!

it is 8 pm I have a calc 2 final tomorrow morning and I'm just now trying to finally learn trig subs.

very clear lecture thank you u are amazing keep working the organic chemistry

Thank you for this video! I can't understand what my calculus professor is talking about sometimes and your videos really help!!

1:55 where did dθ come from? (I understand that something has to go there, but I not quite understand the meaning of dθ in this context)

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Professor Organic Chemistry Tutor, thank you for another excellent video/lecture on Trigonometric Substitution in Calculus Two. All students/nonstudents should have a solid understanding of Trigonometry before studying Trig Substitution.. This is an error free video/lecture on RU-vid TV with the Organic Chemistry Tutor.

You are the best teacher I ever had. Thank you for everything you do. Making it look so easy is probably the hardest part, but it makes all the difference. Screw kahn academy.

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Awesome video but in the last example isnt it supposed to be 1/3sqrt(9+x^2)(-x^2-18) + C? Im just wondering because the - on the x int the x^2-18 part was lost

7:23 Timestamp

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2:37 was my favorite part 👌

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You are a lord and savior I was stuck on this

Can’t you just use u sub by doing some clever manipulation to the u statement?

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posto x=2sint...ho -ctgarcsin(x/2)-arcsin(x/2)....-sqrt(4-x^2)/x-arcsin(x/2)

I lowkey have been watching these even when im not even in math anymore so that i can keep my math skills

Tried the Third problem at the end, solved it, ty!

Better than my professor!

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I with integration by parts am able to calculate it in my mind a lot faster than 20 minutes

Where is the square of the sine in the denominator? U omitted it !

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Thanks professor JG

“So now we gotta do some math” Hm, I had a hunch.

the god tier tutor of the internet

3:05 I'm confused about where the "1 - sin^2 0" came from after "removing a 4". I assume it's by getting the square root of 4, which is 2 and would be put outside of the radical sign, but doesn't that instead come from "sin^2 0 + cos^2 0 = 1" trig identity? The present cosine is off to the side of the fraction. It's like it replaced " - 4 sin^2 0"

love ur videos man thanks very much my whole confusion is gone

Would there be a problem with giving the answer as: -cot(arcsin(x/2)) - arcsin(x/2) + c Instead of using the triangle?

Never took a trig class before, so y'all already know I'm having a great time in calculus 😂

It's important to make sure in every step That the domains are reasonable In the substitution For example The square root of sec²( theta) Has to be positive So we need to make sure in the substitution To make the restrictions positive

I made a 94 on shell and washer method because of this man. I hope I can do the same with trig sub and integration by parts

I think I understood everything up to turning theta into arcsin(x/2)

I have not met a professor who you have not routinely outclassed

Thank you for this lesson organic chem!

Hi, at the timestamp of 3:32 , did u make a mistake writing 2sinQ instead of 2sin^2 Q , or is that correct?

this video saved me

19:18 can somebody tell why it is x² but not - x²... im confused

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THANK YOU

Why is the last one not 3 (1 + (1/9)x^2) sqrt(9 + x^2) - (sqrt(9 + x^2)/3)

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Students can also use the derivatives of inverse trig functions to recall the proper trig substitutions d/dx arcsin(x) = 1/sqrt(1-x^2) d/dx arctan(x) = 1/(1+x^2) d/dx arcsec(x) = 1/(x * sqrt(x^2 - 1)) hyperbolic substitutions, too a*sinh(u) for a*tan(u) a*tanh(u) for a*sin(u) a*cosh(u) for a*sec(u) And you’ll see similar patterns with derivatives of hyperbolic trig functions

for the first one, can you replace 1-sin^2theta with cos^2theta and integrate cot^2theta