Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    10
    ReputationRep:
     \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
    Offline

    19
    ReputationRep:
    (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
    • Thread Starter
    Offline

    10
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (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
    • Thread Starter
    Offline

    10
    ReputationRep:
    (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)
    Offline

    19
    ReputationRep:
    (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?
    Offline

    19
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (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
    • Thread Starter
    Offline

    10
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (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
    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
    • Thread Starter
    Offline

    10
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (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)
    • Thread Starter
    Offline

    10
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (Original post by Gome44)
    Yep of course I know it, i have already used your fourier series one
    very good

    I hope you are enjoying Maths and Oxford.

    All the best!
    • Thread Starter
    Offline

    10
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (Original post by Gome44)
    Analysis suuuuuuccccckkkkkkkssssssss, the rest is bae though. Oxford is quality, lots of wine has been consumed
    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
    • Thread Starter
    Offline

    10
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (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 !!!
    Offline

    18
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (Original post by Gome44)
    I look forward to it
    Here they are ... Freshly baked this evening ... they are not hard,
    I hope you do them (free proof reading needed) before I add them in to my examplebook.

    all the best
    Attached Images
  1. File Type: pdf Question 1.pdf (235.1 KB, 63 views)
  2. File Type: pdf Question 2.pdf (118.1 KB, 54 views)
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 7, 2016
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.