Double integrals: Volume between two surfaces

[@DrChrisTisdell]

Great! Hope you find the free ebook of some use where there are more examples. The link is in the description.

[@DrChrisTisdell]

While $z = _(x^2 + y^2)$ is just a parabola rotated around the Z-axis, but "upside down" when compared to the above parabola in my previous post. Hope this points you in the right direction. Like I said, if you're at UNSW then look back to your notes from earlier this semester or last year.

[@emmaxu6030]

Can you explain why z1-z2 is just the required region? Is that a theorem? How about double (z2-z1, should that the same region?

[@cizma27]

The paraboloid that has extrema or origin point (it's the same point) higher is always first.

[@DrChrisTisdell]

Thanks!! I am also planning to upload full lectures on vector calculus in the near future. The videos will be on another site because they are more than 10 minutes each, but I'll let you know when they are available.

[@DrChrisTisdell]

Hi Steve, I've seen similar questions on previous Class Test 2 schemes, but would be at the higher end of the range of difficulty.

[@DrChrisTisdell]

Moo: If you can sketch a parabola (in 2D) then it's not a big leap to paraboloids in 3D. If you're at UNSW then look back to your MATH1231 notes, week 1; OR, look at my MATH2019 notes, lecture 1, week 1 on My eLearning. If you're not at UNSW, then fear not. A basic rule with simple paraboloids is that the surface is just a parabola rotated around an axis. The axis of rotation is the variable that DOESN'T have a squared sign. Thus, $z = x^2 + y^2$ is a parabola rotated around the Z-axis.

[@DrChrisTisdell]

Hi - it's hard for me to fully understand the nature of your question. What do you mean by "an extra"? An extra what?

[@DrChrisTisdell]

Interesting. I see you are a handy guy to know! I'm still experimenting with these vids and will keep a lookout for Smartboards around campus.

[@DrChrisTisdell]

Hi - you need to be able to draw a picture (or have a good idea of the behaviour of each surface).

[@sjjna]

How exactly did you get your R values??

[@Chamorizard]

Hey! i did the same problem but insted of subtracting z2 and z1 for the fuction, i just put (x^2 + y^2 )dxdy and then did the polar change. I've got the same thing as you but not sure if i can do that :). . soo. . . can i?? :)

[@moopoo123]

hardest step is to be able to visualize the paraboloids, which i still cant do. any tips?

[@Alberto-hd8pt]

Why didn't you multiply the expression by the Jacobian? I mean when you did the change to polar coordinates

[@mohitkulkarni1148]

r is the Jacobian

[@Kudravets-Diana]

Can someone help me how to find the volume between this two balls: r=a r=2acos(theta) ? 😭

[@aeoelvis]

Where did they (1/4) come from?

[@mariogabrielarandacajide5857]

Muchas gracias, sigue haciendo videos así. Saludos desde Paraguay

[@janetlorena5710]

Oohhh otro Pyo saludos xD

[@DrChrisTisdell]

1/2 - 1/4 = 1/4 from the integration involving r.

[@LKGAMER26]

why cant we directly substitute 2pi*r to d(theta)?

[@Sndpkumar100]

if the disk was other than circle...how to do that

[@moopoo123]

ahh cool. thanks for pointing me in the right direction. ill be sure to read up on the notes. its really useful how ur there to answer our youtube questions promptly! cya at the next lecture

[@DrChrisTisdell]

Good to know that it helped!

[@DrChrisTisdell]

Fear not, Readert. I'm sure the SSS will continue as it can do things that my vidoes can't (like immediate Q&A, verbal discussions etc.) I must say that it looks like MATh2019 students are using this channel as a resource in greater numbers than the SSS at this stage of the semester.

[@woo216]

what if the intersection is an eclipse!! PLEASE HELP

[@DrChrisTisdell]

I thought that's what you meant (but wasn't quite sure)..Excellent question. It is a little difficult to explain here, but if you watch /watch?v=TFWYPe3ksJY and skip to 04:53 then you can see why the extra "r" appears. Basically it involves the area for a "polar rectangle".

[@DrChrisTisdell]

Great! Happy to help!

[@emilymbwiga9761]

How about y=x^2 and y=8-x^2 and z=16xy +200

[@mohamedthasneem7327]

Thank you very much sir

[@Dakiller1243]

thanks doc

[@meeeeeert]

right on! helpful

[@xhelixshotx]

This doesn't look like a 2008 video

[@cecilperdue8724]

I know right? The quality of this video comparatively with the videos other people were putting out at the time on their flip phones, it's impressive. He must have used an actual camera. Crazy

[@LKGAMER26]

why cant we directly substitute 2pi*r to d(theta)?