❖ Double Integrals - Changing Order of Integration - Full Ex. ❖ 

😂😂yes

Amen to that

Here I'm doing Economics and need to learn this -__-

14 years later 🤩

jesus christ im here for engineering calculus...

SkyArtineer Try to not think of things in terms of how this is easy and how your professor teaches you something confusing. Remember that the professor is giving the information for a mathematics major- so for us, we need to have all of these other details. Patrick is (excellently) teaching applied mathematics here, not mathematical theory. With an understanding of theory, you should be able to apply it to anything. Its like the difference of being told how to cook a specific recipe, vs. being taught why certain spices go together and methods, and knowing how to cook anything.

Timo Lee Agreed. I highly doubt some random guy saying he "understands this" after watching this video means that he knows it or even did well when tested on it. It just means you can look at it systematically or easily. However you have to know how to comprehend the entire process to apply it with 100% mastery. Even as a non-math major I understand this pretty easily. It helps a little bit to see all the steps properly but would I say that I now understand this? Nope. It's just in my short-term memory.

+Praetorian You guys really showed him!

exactly but my professors just focus so much on the theory and forget about how students should apply and eventually gives us very hard exams (and i mean really very hard) that we cant solve ? trust me knowing the theory without knowing how to apply is just useless so i watch professor which actually gives me the theory in a better way and gives examples but takes a long time

SkyArtineer hahahuwwhahahauahahahaa so true this nutty profs want to explain things to you that would take you at least 30 years experience in maths

happy to help :)

haha q aap ki universty k professor thk ni hen?

good luck!

You probably didn't set up the new integral correctly: The flipped area of integration (i.e. dydx) has to be broken into 2 integrals. ...= \int_{0}^{1}\int_{1}^{2} sin(x-y)dydx + \int_{1}^{2}\int_{x}^{2} sin(x-y)dydx The only other "tricky" part is recognizing that sine is odd and cosine is even (i.e. sin(-x)=-sin(x), cos(-x)=cos(x)) Both methods should yield you ...= sin(2)-sin(1)-1

You divide the area into two parts and add two integrals (one integral for each part)

+gains You are integrating over the same region that was expressed before you decide to change the order of integration. Therefore, you are using the same boundaries of integration. On one of the boundaries, as the x goes from the "top" to the "bottom," the y has it's own value on the curve/line. This is why you change them.

+gains The limit of the first integral are the curves themselves The limit of the the second integral are points. This way, your final result should be be a scalar multiple after integrating x and y on f(x,y)

thanks a lot man :')

Legend

og

You can become a patreon and support him Link in the description

@@Atlas92936 nah, he mean with words. He doesnt want to spend 1$ to thank a guy or else he wouldnt say he didnt know how to thank him!

Me too

Same

Me too

me too

Me too

@@bobby_fett yes !!!

@@KumarHemjeet You haven't felt your comment to be wrong yet? After 4 years...

@@jayanstanite aah..not exactly.

@CLaW PUBG Gaming yes bro ..aah feeling nostalgic.

@@KumarHemjeet If you could go back in time would you still choose to major in engineering? Just curious

College*

Cause no diploma just by watching youtube. Sad but true

Did you pass the exam? I hope you did!!

I really did, though not with the grade I was pursuing ;)

hope u done with your engineering degree by now

@@ibrahimsakr7461 and have a wife and kids