Trig substitution integration: x=a*secθ, calculus 2
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- čas přidán 24. 06. 2024
- Trigonometric Substitution, calculus 2, 4 examples for secant substitution.
0:00 When do we use x=a*secθ?
0:34 Integral of 1/(x*sqrt(x^2-a^2)
3:56 Integral of 1/(x^2-1)^(3/2)
9:07 Integral of sqrt(x^2+2x) hard
17:41 Integral of sqrt(x^2-16)/x^3
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We are currently learning about arc length and reparameterization in my calc 3 class, so this is very helpful! Thank you!
I'm here! Because I was waiting for your great series, substitutions series!
Awesome
Professor Black Pen Red Pen, thank you for the video. A Constant of Integration is needed after the Integration is performed. Please correct these errors in the video.
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Youre such a W guy fr. Needed this for my exam
I really needed to brush up on this topic in particular, am doing vector Calc right now before going into upper division classes and this kind of thing is popping up quite often
The channel where i really understand it 🥲
Our prof didnt told us we need identities no wonder we cant answer it even there are choices 😆 we only pray then roll to pick which letter we should put 😆 now we can atleast attempt which is which 😆
Hello here,, using different methods for integration do we get the same answer with same question???
Thank you sir
Question:
If the integrant appears to the answer of the integral, I think, it's the good thing!
It's the good thing or what ❓
And this thing in somehow is strange to me (for Exp function it's okay, but for another function ... !). At this situation we have an important hidden point or ... ❓
Please talk about it.
Thank you
Hey maybe I missed something. Just wondering at 14:15 how you got ½ln|sec+tan| when integrating sec. Where does the ½ come from?
Thanks for your videos, they are helping me so much.
Ignore me, I was doing integration by parts wrong this whole time.
No please someone explain it Im new to integration
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I have just finished learning integration in my class, and now it's like I am doing a revision of these basic properties.
Edit: By basic properties I mean the first question of his his recent integration videos. So please don't tell me in comments that it's not basic properties.
I'm curious to see how u-sub would be used in the last example here
shouldn't we use the absolute value with √((atan(¶))²)=|atan(¶)|
Can you do integrals of integrals too ❓
Yes. It is called a double integral, or an iterated integral.
A double integral has two different differentials. An application of which, is finding the volume beneath a surface in 3-dimensions, where you integrate z as a function of x treating y as a constant, and then integrate again as a function of y, treating x as a constant. There are also triple integrals, an application of which is integrating relative to all 3 of x, y, z as spatial coordinates in each individual integral, when the integrand might represent a non-uniform density, and you are integrating to find total mass.
An iterated integral has the same differential repeated twice. An application of which, is finding the position function of time, given the acceleration function of time. Both integrals have a dt term. When you integrate the first time, you end up with a constant of integration C1, and when you integrate a second time you get a second constant of integration, C2. You also integrate C1 to get C1*t, so now you have two constants of integration to find. You might know initial velocity and initial position to solve for them, or position at two different points in time.
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