Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacadem... Introduction to trigonometric substitution
Thank you now that I understand the patharoris triangle, I don't have to memorize anymore, I simply use your method from the beginning. This has made my day. Thank you will use this future..
i knew it had to do with the pythagorean theorom and trig and stuff, but people online just kept saying "ok so basically memorize this and ye when u see this do this, when you see this do this, and when you see this do this"
Well yea this one was just probably picked as an easy example. I mean this is a well known integral to begin with lol integral of 1/sqrt(a^2-x^2) = arcsin(x/a)
Question for the first example could you not substitute x to be 2cos(theta) as well because 1-cos^2(theta) = sin^2(theta). Then eventually your answer will result in terms of cosines???
I was expecting the stuff like "substitute x with tanθ" kinda questions when i searched this topic tbh- I didn't knew these formulas had this kinda background 👀 If anyone knows bout what I'm rendering to, pls do name it so that i can search it up- Atleast within a month of this coment getting pasted (I've exam) 👀
This is shady, if you make the adjacent side be x you get some negative thingis, what is shady is that you did not explain why you made the other side be x
Yeah so this is 3 years late, but I think if you're going to make the sine sub you must do the opposite side. If you do adjacent I think you get some arccos stuff. I dunno if it's explicitly wrong, just how he solved it
x would always be less than the adjacent side in this case, but if x be in the front it would be something like x^2 + c^2 and you use 1+tan^2(theta) = sec^(theta), but if you were talking about x^2 - c^2 where x is less than c, you can't use trig sub, but you need to use what's called hyperbolic sub (because if x is greater than adjacent it wouldn't be a point in the circle anymore,, hyperbolic function is another counterpart of trigonometry, they have similar name with them but you add -h to imply that it's hyperbolic function, they are : sinh(x), cosh(x),tanh(x),csch(x),sech(x),coth(x). sinh(x) is defined as (e^x - e^(-x))/2, cosh(x) = (e^x + e^(-x))/2 , the rest you should know with trigonometry definition (and try to come up with some hyperbolic identity, they are needed to solve something like integral(x^2 - c^2)). They are not made up function, you will be mind blown to know that trigonometric function and exponential function can be related by a very special number, and by using that number hyperbolic function definition with euler number can be found.
that's what confused me also, the truth is you can do it both ways the answer will only differ by a constant -arccos(x/2) + c and arcsin(x+2) + c. If you plot those two function they will look the same
@@flownmoon5444 I know I'm late but doesn't it kind of matter if it changes what is adjacent to theta? How I'm confused is how he chose the adjacent side to be the sqrt(a^2-x^2) as opposed to the opposite side?
OMG. I remember this from undergrad years ago. I’m glad this is in my rear view mirror. Good luck to anyone taking integral calc now! Don’t give up!
Thanks bozo
An entire lesson of calculus that went halfway over my half-asleep head, explained perfectly in under 9 minutes. Huzzah!
This is the best explanation of trig substitution on youtube!
Thank you now that I understand the patharoris triangle, I don't have to memorize anymore, I simply use your method from the beginning. This has made my day. Thank you will use this future..
patharoris ???
@@IStMl Thank you that was 1 year ago, how about Pythagorean.
Seriously?!Patharoris?
Lmao the patharoris triangle😂😂
ok
You've saved my midterm. A true legend
This is exactly what I was looking for. Thank you Sal!
Prof. was explaining this for 70 min, and I did not understand anything. The 9 min video saved my life.
i knew it had to do with the pythagorean theorom and trig and stuff, but people online just kept saying "ok so basically memorize this and ye when u see this do this, when you see this do this, and when you see this do this"
Same bro same...
I came to know this is supposed to be different while solving questions and asking doubts online (google and stuff) r8 before exams-
Best professor I've ever had right here 💰💰
This is excellent!! Thank you.
Wow..thanku soo much..this video helped me a lot ❤️🔥
I was really confused for a while cuz your '4' looked like a 'u' to me......
He says it's square root of 4 - x^2 in the beginning
Now that u said it, I can't stop but sees 4 as u now ;-;
Missed the beginning as well and thought it was u as well
For me doing trigo subsitution,I will think about how to get rid of the sqrt first just like 3:06 I straight away let x=2sinø then sqrt(4-x²)=2cosø
you can just do it by factorising 4 and substituing by ( x/2)
Buzz kill
That's what i was thinking two
Well yea this one was just probably picked as an easy example. I mean this is a well known integral to begin with lol integral of 1/sqrt(a^2-x^2) = arcsin(x/a)
I love his voice
Great vid!
thank you for the explanation
Clear and concise.... Thanx!
Question for the first example could you not substitute x to be 2cos(theta) as well because 1-cos^2(theta) = sin^2(theta).
Then eventually your answer will result in terms of cosines???
X can’t be sin and cos at the same time? Right?
Thank you bro !
i didn't it at the first time of seeing this but thank you for explaining
Great video!
why does this only have 2000 views considering he has over 2.000.000 followers???
Dan Alexander how many people actually need help with calc 2 material. Khan academy teaches algebra 1 and even lower math I believe.
I got an A in differential calculus and an A in integral calculus. Have fun to everyone who is doing this topic. 🤣
can we solve the sinh(x) and the rest of the conditions and the inverse with the same rules? i mean is it ok or is it depletable and thanks
You can solve certain integrals by substituting in hyperbolic functions. Probably not this one, though.
Why did you use 2 on the hypotenuse, where did you derive it
It comes from the Pythagorean theorem, c is the hypotenuse the longest side
Bless u
I was expecting the stuff like "substitute x with tanθ" kinda questions when i searched this topic tbh-
I didn't knew these formulas had this kinda background 👀
If anyone knows bout what I'm rendering to, pls do name it so that i can search it up-
Atleast within a month of this coment getting pasted (I've exam) 👀
it's perfect
This is shady, if you make the adjacent side be x you get some negative thingis, what is shady is that you did not explain why you made the other side be x
yea i did the same thing with the adjacent side and i got weird shit
tru i got -arccos(x/2) + c
Yeah so this is 3 years late, but I think if you're going to make the sine sub you must do the opposite side. If you do adjacent I think you get some arccos stuff. I dunno if it's explicitly wrong, just how he solved it
x would always be less than the adjacent side in this case, but if x be in the front it would be something like x^2 + c^2 and you use 1+tan^2(theta) = sec^(theta), but if you were talking about x^2 - c^2 where x is less than c, you can't use trig sub, but you need to use what's called hyperbolic sub (because if x is greater than adjacent it wouldn't be a point in the circle anymore,, hyperbolic function is another counterpart of trigonometry, they have similar name with them but you add -h to imply that it's hyperbolic function, they are : sinh(x), cosh(x),tanh(x),csch(x),sech(x),coth(x). sinh(x) is defined as (e^x - e^(-x))/2, cosh(x) = (e^x + e^(-x))/2 , the rest you should know with trigonometry definition (and try to come up with some hyperbolic identity, they are needed to solve something like integral(x^2 - c^2)). They are not made up function, you will be mind blown to know that trigonometric function and exponential function can be related by a very special number, and by using that number hyperbolic function definition with euler number can be found.
that's what confused me also, the truth is you can do it both ways the answer will only differ by a constant -arccos(x/2) + c and arcsin(x+2) + c. If you plot those two function they will look the same
Why does "x" have to be on the vertical leg?
Vincent Nguyen does not matter
@@flownmoon5444 I know I'm late but doesn't it kind of matter if it changes what is adjacent to theta? How I'm confused is how he chose the adjacent side to be the sqrt(a^2-x^2) as opposed to the opposite side?
@@TheTacticalMessHave you figured it out? I could use your help
@@TheTacticalMessif u have x be the hortizonatal leg, theta will be the top angle 📐
why hypotenuse is 2 in the first place?
It's because the square root of 4 is 2
Ehy this substiturion is for actue angles inly what about obtuse angles?
Every obtuse angle can be redefined as the sum of kpi/2 + some acute angle which will return the same value as the obtuse angle.
How/Why did he have 2 in the Hypotenuse? Where/how did he get that?
From the 4 in the bottom of the original equation. Sqrt (4) = 2. Think a^2 + b^2 = c^2. Where c^2 equals 4.
03:19 If x = 2sinΘ then dx = 2cosΘ dΘ - why?
dx = derivative of x, derivative of sin is cos so derivative of 2sin(theta) = 2cos(theta) and a d(theta) to replace dx
Algebraic way of seeing it:
x=2sin(t)
dx/dt=2cos(t)
dx=2cos(t)dt
I love math
okay vid!
Sal i still couldnt see the trees for the forest lolp
4:46 when you say "this equals to dBETA" i thought u said debata which translates to english into "debate"
Theta, not beta.
I love you.
eerie noise at @4:48 anyone?
oh lol, i hear it too
o
That is not a 4. that is a u. If you going to teach, don't be so sloppy. Your learners need to be able to see what you have written. Come on now.
In the first 8 seconds he says its a 4
First lol
Christ is coming soon believers lets get prepared
Amen brother.
Its not hard task..so easy math.
why are you here then?
Lol