holy fuck if that one problem took you 20 minutes to do by hand, i hate to imagine how long it would take us mere mortals. probs an hour. calculators would of halved that time at least
he is actually solving it with giving us instructions on how to. So it would actually take his 10 mins at most if he was solving it during an exam or something.
Wow. The first half of the first video was all I needed to know about the concept of substituting polar variables and the rest of the series was solving the giant integral lol. This is one of the longest integrals I've seen lol.
Mistake- you added 1/2 to the 1 and got 3/2, but you didn't take out the + 1/2 in the equation even after adding it. That threw me off >< thanks for making so many great videos though!
@napplez this is a good example because doing this from the center at (0,1) is different than (0,0). With the center at (0,1) the limits of integration has sin(theta) while the at (0,0) would not. I feel that this is important to learn because it shows a limit of integration as a variable. Keep it up Pat!
How come 6x+4y+z=12 == 6x+4(y+1)+z=12 ?? I think you meant 6x+4(y+1)+z=16 Furthermore, in the first video he got the intervals using x^2+y^2=2y not 6x+4y+z=12. I'm kinda confused :/
Does patrick get funding if the viewer uses ad blocking software? JW bc I would feel bad using the videos but not "giving back" to the man that's giving so much.
I am actually glad you took such a long example, it really helped me to understand how every step works, thanks!
dude you need to add ad's in the beginning of your video, you deserve any amount of income you can get for helping us students
This example was very helpful - thank you for taking the time to go through each step, no matter how simple.
We are calculating a cylinder here, that goes up the z-axis with the circle x^2+y^2=2y as its base.
I love you, you awesome human!! thanks for saving my engineering degree
I'd actually slap my lecturer if he gave this in an exam...
it's actually an easy problem, just a long one then again it depends on ur level of studies
i'd probably thank him a lot instead, because basically you are just doing integration here, which is pretty much elementary school.
But it's time consuming.
So? was it on the exam?
did you do it? if u did pls record I want to watch tho
holy fuck if that one problem took you 20 minutes to do by hand, i hate to imagine how long it would take us mere mortals. probs an hour. calculators would of halved that time at least
he is actually solving it with giving us instructions on how to. So it would actually take his 10 mins at most if he was solving it during an exam or something.
@napplez nice observation!
Wow. The first half of the first video was all I needed to know about the concept of substituting polar variables and the rest of the series was solving the giant integral lol. This is one of the longest integrals I've seen lol.
what was the question? ı really forgot
thanks! ya, i made that mistake in part2! ops! oh well, i hope it still helps with that one exception!
Gawd its a long problem! Kudos Patrick
Thank you so much Patrick. I understand it completely now.
wow this stuff looks complicated lol but ill refer to your vids when I am introduced to this stuff:P
That really helped me a lot. I have an exam today. I hope that will give me a perfect score. LOL!
This has been so helpful!!!
perfect! :)
Excellent. Thanks.
pat the man what a warrior
awesome video! Is there a general formula or proof for calculating double integrals from Polar coordinates into Cartesian coordinates?
I love my ti 89
Mistake- you added 1/2 to the 1 and got 3/2, but you didn't take out the + 1/2 in the equation even after adding it.
That threw me off >< thanks for making so many great videos though!
everyone says everything is easy AFTER they know it... human nature to try and at least look smart i think : )
patrick
i was wondering at around 2:30 u said that integral of 2*cos(2theta) is -sin(2theta)
can u please explain a bit to me in detail??? thanks
@napplez this is a good example because doing this from the center at (0,1) is different than (0,0). With the center at (0,1) the limits of integration has sin(theta) while the at (0,0) would not. I feel that this is important to learn because it shows a limit of integration as a variable. Keep it up Pat!
hmmm isnt the volume of a sphere of radius 1 = 4/3pi?
all this =8p
Solid math there
is it just from 0 to pi because its a disk?
Now do it in original rectangular coordinates to show if it would take more than 3 videos
I hate math and you do but that what life brought me too
How come
6x+4y+z=12 == 6x+4(y+1)+z=12 ?? I think you meant 6x+4(y+1)+z=16
Furthermore, in the first video he got the intervals using x^2+y^2=2y not 6x+4y+z=12.
I'm kinda confused :/
wtarch again you are confuse please
The integration of the cos is -sin I think
So the derivative of -sin is what then?
no that is to be its derivation :)
+Omaralfarouq Alfazazi integral of cos is sin, the derivitive of cos is -sin
Than you very much bubby b & ***** .. I hope to bother of you the best :)
np, gl to u 2
I got 4pi/3 .. I saw in the second video that you squared a term one too many times, was that corrected for? is 8pi definitely the right answer?
Does patrick get funding if the viewer uses ad blocking software? JW bc I would feel bad using the videos but not "giving back" to the man that's giving so much.
Jasmine Lane no
@@xxroyalxtigerxx i think she died bro that was 5 years ago
@@pvzglooper9883 bruh, people can live way more than 5 years. Trust me man, I saw it with my own eyes. It is real
I got 4pi because I the 1/2 wasn't supposed to be squared
Why wasn’t it meant to be squared? Wasn’t the substitution (1/2(1-cos(theta)))^2 ? Which would mean that half is squared when you pull it out?
thank you!!!!!!!!!!!!!!
What’s the final answer?
42
thanks. u. good video
excellent example, thanks
YO BRO VOLUME CAN BE THE SAME JUST MOVE THE CIRCLE TO THE CENTER LOL
i am ben affleck.