Green's Theorem Two Regions (KristaKingMath)

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Green's Theorem Two Regions calculus problem example.
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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[@TahsinEngin-Akademi]

If you change order of integral, ie, dydx instead of dxdy, you would not have to split area into two parts

[@syedshaharyaarhussain8248]

You could have solved this question by considering both triangles as single triangle as well. For this purpose take dx first then dy. Limits of "x" will be from (y) to (2-y) and limits of "y" will br from 0 to 1. Solving question by this method will remove the hectic of such a large number of fraction which you have to sum up to get answer.

[@21mejia25]

I was thinking the same thing. I’ll have to try it on paper

[@toshi2252]

yeah ull get the same answer

[@HeyKevinYT]

Yep, it gives 3 also

[@81546mot]

Great job! Looking forward to more of your math videos. You explain things well.

[@PtotheMtotheJ]

This channel is my go-to for math videos. Thanks!

[@kristakingmath]

PtotheMtotheJ :D

[@kristakingmath]

Thank you so much!! :D

[@adriancho07070707]

@TheIntegralCALC Thanks, I just had a test of complex variable this week and needed solved examples of Green's theorem, your video helped a lot

[@adriancho07070707]

@TheIntegralCALC Yes indeed! Thank you and nice to meet you

[@nathanelliott9340]

Great video! I love how you explain so well! Very entertaining as well!

[@kristakingmath]

Thanks Nathan!

[@kristakingmath]

@adriancho07070707 I'm writing in Sketchbook Express. I like it a lot! :)

[@aymanadel3470]

You are way of learning is outstanding. I hope that our professors do like you by completing the solution up to the end. I hope you are ok.

[@kristakingmath]

Glad I could help! :)

[@MR-kk5bf]

You are angel

[@katherine4386]

Awesome!

[@VillegasCar]

demasiado bueno!!!

[@kristakingmath]

@adriancho07070707 I'm so glad! I hope you did well on your test!

[@marwaahmed7897]

Amazing😍😍😍 ... wow!! Your explanation wow!!!!😭😭😭😭

[@ALIENGOATMESSI]

that bye bye at the end

[@drewgraham1482]

Great video, thanks!

[@kristakingmath]

+Drew Graham Glad you liked it!

[@brendarustein2017]

thanks a lot for your videos they're awesome! I hope you can help me in that question... I have to calculate the integral:(e^y-tanx/2)dx+(xe^y+ycosy^2)dy where c is the region bounded by the curves y=x^2 and y=8-x^2 in the first quadrant. but the substract of the derivatives of q in respect to x and p in respect to y equals 0 which means that the integral of 0 is just a constant C but then I cannot continue... I hope you can help me thanks

[@ScholarStream_25]

She made even more interesting . thanks

[@lofi_song562]

Nice 👍🏽

[@brendarustein2017]

thanks for the quick answer! that's exactly the same thing I thought to do but then I cannot understand why the answer is 0.5sin64 because I even haven't a trigonometric function in the integral! is that maybe a mistake?Because we solved this in the same way... of course thanks for your answer

[@susanbenmark3890]

Swing black triangle

[@haider3936]

very very nice i did get so much

[@adriancho07070707]

What kind of software did you use? Looks pretty useful, nice explanation by the way, greetings frome Mexico

[@dubey_ji]

I just love her voice .... And yeah she explained nicely . That's the reason I don't watch mit opencourse ware videos anymore . 😅😅😅🙄🙄😑😑

[@jingyucai4915]

I guess you can simply do dxdy instead of dydx and it would not require separation of the integral

[@meghayadav8436]

Thank you

[@kristakingmath]

You're welcome, Megha! :D

[@624salamashah6]

Thank you so much mam

[@kristakingmath]

You're welcome, Salama! :)

[@davisnganga6266]

Thanks for this madam

[@kristakingmath]

You're welcome, Davis! :)

[@engineerhere1061]

Love u so much dear

[@jacklo8198]

What would look like if green theorem in vector form?

[@Zayneakajordan]

Can you do something specifically on Stokes, and the Divergence theorems?

[@kristakingmath]

It's on my list! :)

[@kristakingmath]

It's always possible that the answer is wrong... but I can't see how they got (sin64)/2! :)

[@gopinkle3481]

Do you know how to get rid of the texts that are obstructing our views of your presenration.

[@aymanadel3470]

Thanks!

[@kristakingmath]

You're welcome, Ayman! :)

[@aymanadel3470]

@@kristakingmath I'm so glad to be with such an amazing teacher. By the way, I usually face some diffeclates about "Differential Equation" how can I get your help? For example; can I put my question s here? or how

[@aymanadel3470]

@@kristakingmath but if you cannot handle it, do not worry it is ok.

[@ismailkhan-bc3pz]

Hey, I decided to evaluate the triangle as a whole by treating the double integral as type 2 i.e(dxdy) and I got -3. Why did I receive a negative answer?

[@ghadaalfraih312]

You should get a positive 3 if your limit order is correct. You probably did it clockwise instead of counter clockwise, which would explain the opposite sign. Proper limits: 0≤y≤1, y≤x≤2-y or: 1≤y≤0, 2-y≤x≤y

[@sarbjotsingh5474]

mother of calculus ...............thanks

[@kristakingmath]

+Sarbjot Singh you're welcome!

[@heinerborrero913]

I love you

[@victormvaldez6393]

What’s the name of the program ?

[@mahmoudm451]

What if we took the double integral with respect to x first (dxdy), doesn't that make it 1 integral only?

[@jamieducator]

Yes you can do that... But in this case you have to take the limits in terms of y.

[@nabihasan9893]

Great. Please help me, how you write this, which app you are using?

[@kristakingmath]

Hey, Nabi! It's called Sketchbook. :)

[@Noahmalacad]

perfect

[@kristakingmath]

Thanks, Noah! :D

[@kristakingmath]

You should have integral (from 0 to 2) of integral (from x^2 to 8-x^2) of 0 dy dx, right? Okay, so when you take the integral of 0, you just get a constant, like you said, let's just call it n. You can't evaluate n on the range x^2 to 8-x^2, so you're just left with n, and now you have the integral (from 0 to 2) of n dx. Now, when you integrate with respect to x, you get nx, on the range 0 to 2. Plugging in limits of integration, you get 2n-0n, or just 2n. Hope that helps! :)

[@samde3000]

Muy útil

[@kristakingmath]

I'm glad it helped, Samuel! :)

[@arunmadhavan4457]

Isn't the area of that triangle just 1? because, when you look at it, it has a base of 2 and a height of 1. 2 x 1 = 2. 2 x .5 = 1

[@doggiegirls]

its a LINE integral.

[@waldenfreedman3457]

It's easier to do the double integral in the order dx dy. Then no need to break into two separate integrals.

[@zetch972]

I agree, she could have just inverted the integral.

[@stephensewe4774]

sir, Good work done . Please what application did u use in the presentation . i wanna use it for teachings in class

[@kristakingmath]

I explain here :) www.kristakingmath.com/blog/how-i-create-my-videos

[@susanbenmark3890]

Pm

[@susanbenmark3890]

Ý

[@bessamin3859]

the answer will be 0.8333

[@susanbenmark3890]

🪄📀KOVERT

[@susanbenmark3890]

🪄Dr.

[@pspmaster2071]

can't you just multiply area of left triangle by two?

[@garfieldhu]

pspmaster2071 no. The integrand is not constant.

[@susanbenmark3890]

Allah

[@susanbenmark3890]

¹Zk

[@susanbenmark3890]

🪄^Outline