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     \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
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    (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
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    (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
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    (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
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    (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)
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    (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?
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    (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
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    (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
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    (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
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    (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
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    (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
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    (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)
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    (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
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    (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!
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    (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
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    (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
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    (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
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    (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 !!!
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    (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 ****


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    (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, 54 views)
  2. File Type: pdf Question 2.pdf (118.1 KB, 44 views)
 
 
 
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