Compute $iint_S xz^2dydz+yz^2dzdx+z^3dxdy$Outward Flux of a Divergenceless Vector Field on an EllipsoidSurface integral over an inconvenient surfaceWhat does $iint_S (hatmathbfn times nabla psi) ; dS$ mean?Surface integral problem $displaystyleiint_Sx^2dS$Evaluating the surface integral side of a divergence theorem problemChange of Variable vs ParametrizationHow to calculate the integral on surface which cannot be expressed in functions easily?Heat flow surface integral problemsurface integral of angle between fixed vector and the unit normalSurface integral with cylinder-form surface.
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Compute $iint_S xz^2dydz+yz^2dzdx+z^3dxdy$
Outward Flux of a Divergenceless Vector Field on an EllipsoidSurface integral over an inconvenient surfaceWhat does $iint_S (hatmathbfn times nabla psi) ; dS$ mean?Surface integral problem $displaystyleiint_Sx^2dS$Evaluating the surface integral side of a divergence theorem problemChange of Variable vs ParametrizationHow to calculate the integral on surface which cannot be expressed in functions easily?Heat flow surface integral problemsurface integral of angle between fixed vector and the unit normalSurface integral with cylinder-form surface.
$begingroup$
Problem
Compute
$$displaystyle iint_S xz^2dydz+yz^2dzdx+z^3dxdy$$
where $S$ denotes the outside surface of the common part $Omega$ of $x^2+y^2+z^2leq R^2$ and $x^2+y^2+z^2 leq 2Rx$.
Comment
It would be fair to say this could be solved by Gauss's Formula, but how to make the transformation? Anyone can do me a favour?
integration multivariable-calculus surface-integrals
edited Feb 1 at 13:48
Martin Sleziak
44.8k10119273
asked Jan 21 at 5:12
mengdie1982mengdie1982
4,932618
$endgroup$
add a comment |
$begingroup$
Problem
Compute
$$displaystyle iint_S xz^2dydz+yz^2dzdx+z^3dxdy$$
where $S$ denotes the outside surface of the common part $Omega$ of $x^2+y^2+z^2leq R^2$ and $x^2+y^2+z^2 leq 2Rx$.
Comment
It would be fair to say this could be solved by Gauss's Formula, but how to make the transformation? Anyone can do me a favour?
integration multivariable-calculus surface-integrals
edited Feb 1 at 13:48
Martin Sleziak
44.8k10119273
asked Jan 21 at 5:12
mengdie1982mengdie1982
4,932618
$endgroup$
1
$begingroup$
but the notation is not wrong.
$endgroup$
– mengdie1982
Jan 21 at 5:18
$begingroup$
@DavidG.Stork: The OP's notation is absolutely fine, and you're completely wrong. Please study the subject yourself before claiming something invalid. See, for example here and here.
$endgroup$
– zipirovich
Jan 21 at 6:17
add a comment |
$begingroup$
Problem
Compute
$$displaystyle iint_S xz^2dydz+yz^2dzdx+z^3dxdy$$
where $S$ denotes the outside surface of the common part $Omega$ of $x^2+y^2+z^2leq R^2$ and $x^2+y^2+z^2 leq 2Rx$.
Comment
It would be fair to say this could be solved by Gauss's Formula, but how to make the transformation? Anyone can do me a favour?
integration multivariable-calculus surface-integrals
edited Feb 1 at 13:48
Martin Sleziak
44.8k10119273
asked Jan 21 at 5:12
mengdie1982mengdie1982
4,932618
$endgroup$
Problem
Compute
$$displaystyle iint_S xz^2dydz+yz^2dzdx+z^3dxdy$$
where $S$ denotes the outside surface of the common part $Omega$ of $x^2+y^2+z^2leq R^2$ and $x^2+y^2+z^2 leq 2Rx$.
Comment
It would be fair to say this could be solved by Gauss's Formula, but how to make the transformation? Anyone can do me a favour?
integration multivariable-calculus surface-integrals
integration multivariable-calculus surface-integrals
edited Feb 1 at 13:48
Martin Sleziak
44.8k10119273
asked Jan 21 at 5:12
mengdie1982mengdie1982
4,932618
edited Feb 1 at 13:48
Martin Sleziak
44.8k10119273
asked Jan 21 at 5:12
mengdie1982mengdie1982
4,932618
edited Feb 1 at 13:48
Martin Sleziak
44.8k10119273
edited Feb 1 at 13:48
Martin Sleziak
44.8k10119273
edited Feb 1 at 13:48
Martin Sleziak
44.8k10119273
44.8k10119273
asked Jan 21 at 5:12
mengdie1982mengdie1982
4,932618
asked Jan 21 at 5:12
mengdie1982mengdie1982
4,932618
asked Jan 21 at 5:12
mengdie1982mengdie1982
4,932618
4,932618
1
$begingroup$
but the notation is not wrong.
$endgroup$
– mengdie1982
Jan 21 at 5:18
$begingroup$
@DavidG.Stork: The OP's notation is absolutely fine, and you're completely wrong. Please study the subject yourself before claiming something invalid. See, for example here and here.
$endgroup$
– zipirovich
Jan 21 at 6:17
add a comment |
1
$begingroup$
but the notation is not wrong.
$endgroup$
– mengdie1982
Jan 21 at 5:18
$begingroup$
@DavidG.Stork: The OP's notation is absolutely fine, and you're completely wrong. Please study the subject yourself before claiming something invalid. See, for example here and here.
$endgroup$
– zipirovich
Jan 21 at 6:17
1
1
$begingroup$
but the notation is not wrong.
$endgroup$
– mengdie1982
Jan 21 at 5:18
$begingroup$
but the notation is not wrong.
$endgroup$
– mengdie1982
Jan 21 at 5:18
$begingroup$
@DavidG.Stork: The OP's notation is absolutely fine, and you're completely wrong. Please study the subject yourself before claiming something invalid. See, for example here and here.
$endgroup$
– zipirovich
Jan 21 at 6:17
$begingroup$
@DavidG.Stork: The OP's notation is absolutely fine, and you're completely wrong. Please study the subject yourself before claiming something invalid. See, for example here and here.
$endgroup$
– zipirovich
Jan 21 at 6:17
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Note that $x^2+y^2+z^2 leq 2Rx$.
is actually :
$(x-R)^2+y^2+z^2 leq R^2$.
answered yesterday
Mather Mather
4108
$endgroup$
add a comment |
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$begingroup$
Note that $x^2+y^2+z^2 leq 2Rx$.
is actually :
$(x-R)^2+y^2+z^2 leq R^2$.
answered yesterday
Mather Mather
4108
$endgroup$
add a comment |
$begingroup$
Note that $x^2+y^2+z^2 leq 2Rx$.
is actually :
$(x-R)^2+y^2+z^2 leq R^2$.
answered yesterday
Mather Mather
4108
$endgroup$
add a comment |
$begingroup$
Note that $x^2+y^2+z^2 leq 2Rx$.
is actually :
$(x-R)^2+y^2+z^2 leq R^2$.
answered yesterday
Mather Mather
4108
$endgroup$
Note that $x^2+y^2+z^2 leq 2Rx$.
is actually :
$(x-R)^2+y^2+z^2 leq R^2$.
answered yesterday
Mather Mather
4108
edited yesterday
answered yesterday
Mather Mather
4108
answered yesterday
Mather Mather
4108
answered yesterday
Mather Mather
4108
4108
add a comment |
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1
$begingroup$
but the notation is not wrong.
$endgroup$
– mengdie1982
Jan 21 at 5:18
$begingroup$
@DavidG.Stork: The OP's notation is absolutely fine, and you're completely wrong. Please study the subject yourself before claiming something invalid. See, for example here and here.
$endgroup$
– zipirovich
Jan 21 at 6:17