Integration

Original post by Gome44

\int _{-1}^1\int _0^{\frac{1}{\sqrt{2}}}\int _x^{\sqrt{1-x^2}}x^{2\:}+y^2+z^2\:dydxdz

Im trying to convert to spherical polars but can't work out what the limits should be. Answer should be 5pi/24

@TeeEm

you need to work out the shape first

Reply 2

OP

Original post by TeeEm

you need to work out the shape first

Ah should probably have mentioned its the region bounded by: x^2 + y^2 <1, 0<x<y, -1<z<1

Reply 3

Original post by Gome44

Ah should probably have mentioned its the region bounded by: x^2 + y^2 <1, 0<x<y, -1<z<1

I can see this from the limits ... Some double cone inside a cylinder between -1 and 1

I have to picture it

Reply 4

OP

Original post by TeeEm

I can see this from the limits ... Some double cone inside a cylinder between -1 and 1

I have to picture it

double cone say wut?

I thought it was just 1/8 of a cylinder (unless I've got this horribly wrong)

Reply 5

Original post by Gome44

double cone say wut?

I thought it was just 1/8 of a cylinder (unless I've got this horribly wrong)

I see a double cone inside a cylinder of radius 1 and we are between z = -1 amd z =1, so the cone touches the cylinder at that height.

the integration (volume) region is the space between the double cone and the cylinder (so symmetry)

Is it spherical or cylindrical polars?

Reply 6

Original post by Gome44

double cone say wut?

I thought it was just 1/8 of a cylinder (unless I've got this horribly wrong)

sorry no cone
Plane inside the cylinder
correct 1/8 slice inside

(edited 8 years ago)

Reply 7

Original post by Gome44

\int _{-1}^1\int _0^{\frac{1}{\sqrt{2}}}\int _x^{\sqrt{1-x^2}}x^{2\:}+y^2+z^2\:dydxdz

Im trying to convert to spherical polars but can't work out what the limits should be. Answer should be 5pi/24

@TeeEm

I got the right answer but with cylindrical polars

Reply 8

OP

Original post by TeeEm

I got the right answer but with cylindrical polars

yep i have just done it with cylindrical polars (hence the delayed response). Fairly idiotic on my part, the clue is in the name of the coordinate system...

Thanks for your help :smile:

Reply 9

Original post by Gome44

yep i have just done it with cylindrical polars (hence the delayed response). Fairly idiotic on my part, the clue is in the name of the coordinate system...

Thanks for your help :smile:

no worries ...
in cylindrical, it is fairly pathetic.
I will write tomorrow a beast (cone inside a cylinder), then I will try cone in a hemisphere

Reply 10

OP

Original post by TeeEm

no worries ...
in cylindrical, it is fairly pathetic.
I will write tomorrow a beast (cone inside a cylinder), then I will try cone in a hemisphere

I look forward to it

Reply 11

Original post by Gome44

I look forward to it

You know my resources for undergrads I hope.
(not here but in my site where they get constantly updated)

Reply 12

OP

Original post by TeeEm

You know my resources for undergrads I hope.
(not here but in my site where they get constantly updated)

Yep of course I know it, i have already used your fourier series one :smile:

Reply 13

Original post by Gome44

Yep of course I know it, i have already used your fourier series one :smile:

very good

I hope you are enjoying Maths and Oxford.

All the best!

Reply 14

OP

Original post by TeeEm

very good

I hope you are enjoying Maths and Oxford.

All the best!

Analysis suuuuuuccccckkkkkkkssssssss, the rest is bae though. Oxford is quality, lots of wine has been consumed :smile:

Reply 15

Original post by Gome44

Analysis suuuuuuccccckkkkkkkssssssss, the rest is bae though. Oxford is quality, lots of wine has been consumed :smile:

excellent stuff!!

Analysis was bad for me too, but algebra was even worse...
You get used to it. The first year is always a shock

Reply 16

OP

Original post by TeeEm

excellent stuff!!

Analysis was bad for me too, but algebra was even worse...
You get used to it. The first year is always a shock

Can't wait until second year so I can drop all the pure stuff and live off applied. I quite enjoy linear algebra (hated it at first though), doing groups in two weeks so hopefully it shouldn't be too bad

Reply 17

Original post by Gome44

Can't wait until second year so I can drop all the pure stuff and live off applied. I quite enjoy linear algebra (hated it at first though), doing groups in two weeks so hopefully it shouldn't be too bad

I hope you like them ...
I hated them with a passion !!!

Reply 18

username1162972

18

Original post by Gome44

\int _{-1}^1\int _0^{\frac{1}{\sqrt{2}}}\int _x^{\sqrt{1-x^2}}x^{2\:}+y^2+z^2\:dydxdz

Im trying to convert to spherical polars but can't work out what the limits should be. Answer should be 5pi/24

@TeeEm

Crazy ****

Posted from TSR Mobile

Reply 19