Trig substitution integration: x=a*sinθ, calculus 2
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- Опубликовано: 30 июл 2024
- In this calculus 2 tutorial, we will go over 4 examples on how to use the sine substitution to solve integrals. Use the time stamps below to help you navigate the video.
0:00 When do we use x=a*sinθ
0:49 Integral of 1/sqrt(a^2-x^2)
4:12 Integral of sqrt(2-x^2)/x^2
10:25 Integral of sqrt(1-4x^2)
18:41 Integral of 1/(x*sqrt(9-x^2))
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I don't know how well you know how to teach other aspect of math..but when it comes to math.. i give it to you🎉🎉😊😊
18:50 that moment of realization when u accidentally erased it was too funny
thank you, this is really useful. Revising for my maths final and this is one area I've always struggled with, but after you explained it makes so much more sense!
Man the way you explain this stuff is insane thanks its really helpful !!!
just joined your new channel ......
quality and free calculus for all....
u almost forgot the "+ c!" you ARE human 😂
You are the best ever i saw in math world .i wish can met you one day
wow your videos are very great nice well explained thank u sir🙂
I love your videos
doing three problems like this is helpful for me having attention span issues
These are good, thanks.
8:10 damn i was lost there i was like how can csc^2 become cot but i forgot this was integration not derivative
It's so helpfull
I'm a burnt out cal 2 student and it is wholly disturbing how you simplify this!
in problem 3 shouldnt you have multiplied the x= asinx by 2 to get what 2x is equal to? thank you'
Great Video!!!
That intro is so funny
Just wondering, where did you get your "ultimate calc 2 integrals" poster?
It’s my merch. You can check it out in the description 😃
I can’t buy your merch because it says me that my email address is not valid.😕
Keep your good work!
Wow, super nice
Thank you sir
totally agree!!!
Quick question. If I was in your class and used x = acos(theta) and no errors would you be mad or give full points
Full points.
Pls can u help me this question?
The integration of 2x cube minus 4x minus 8 over (x square minus x)(x square plus 4) dx or
2x³-4x-8/(x²-x)(x²+4)dx
I'm late but
2x^3-4x-8 = 2(x^3-2x-4)
x^2-x = x(x-1)
Take the 2 out
2 × integral of (x^3-2x-4)/x(x-1)(x^2+4)
2 Is is a root of x^3-2x-4, when dividing x^3-2x-4 by x-2 we have the factorization
(x-2)(x^2+2x+2)
So, 2 × integral of (x-2)(x^2+2x+2)/x(x-1)(x^2+4)
Well, I tried to simplify to eliminate some term but I didn't see a way, so lets to partial fractions
(x-2)(x^2+2x+2)/x(x-1)(x^2+4) = A/x + B/(x-1) + (Cx+D)/(x^2+4)
Well, this is the way
Good
Nice job
Good one
🤩🤩🤩😍😍😍
Did anyone else notice the ambulance at around 17 minutes?
Thank you for the video. A plus C is needed after the integration is performed. For example, when you integrate d theta, you have theta, this is incorrect. The correct solution is theta plus a Constant. Please correct these errors in the video.
0:00 i⁴
Can u solve this if solve you are real mathmatician integration 0 to ∞ [ u^(s-1) ]/[ e^(u) + y ] ^(2) du 🥺
my calc 2 professor took the whole hour and 40 minutes to explain this lmao
How do you upload videos on your so many channels regularly? I know you are a math wizard because you use teleportation spell at start of your videos.
Can u solve this if solve you are real mathmatician integration 0 to ∞ [ u^(s-1) ]/[ e^(u) + y ] ^(2) du 🥺
If u solve my problem then I coolbe with u I am also mathmatician I have a theroy to solve Riemann hypothesis 😑
fhuuuuaaaaaghk
Respected sir what's your religion pls reply me. I am mostly watching your video which is very helpful for us may Allah long live you.❤❤❤