Flux outward Sphere-cut

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$D=x^2+y^2+z^2le 8,zge 2F=0,0,z^2/2$



In order to find the flux (out of the boundary of $D$) I used the divergence theorem $div=z$.



Is the flux:



$int_theta=0^theta=2piint_z=2^z=sqrt8int_r=0^r=sqrt8-z^2zrdrdzdtheta = 4pi$



?




integration multivariable-calculus




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  • You forgot to multiply by the Jacobian
    – zokomoko
    yesterday










  • forgot to write it, but I did calculation with it
    – NPLS
    yesterday











  • @NPLS: So please include the Jacobian in your problem statement so that others are not confused.
    – David G. Stork
    yesterday










  • Ok.. another thing: did you mean the flux through the boundary of D? Because when formulating such a question, one needs to specify the surface exactly.
    – zokomoko
    yesterday











  • yes out of the boundary
    – NPLS
    yesterday














up vote
0
down vote

favorite












$D=x^2+y^2+z^2le 8,zge 2F=0,0,z^2/2$



In order to find the flux (out of the boundary of $D$) I used the divergence theorem $div=z$.



Is the flux:



$int_theta=0^theta=2piint_z=2^z=sqrt8int_r=0^r=sqrt8-z^2zrdrdzdtheta = 4pi$



?




integration multivariable-calculus




share|cite|improve this question





















  • You forgot to multiply by the Jacobian
    – zokomoko
    yesterday










  • forgot to write it, but I did calculation with it
    – NPLS
    yesterday











  • @NPLS: So please include the Jacobian in your problem statement so that others are not confused.
    – David G. Stork
    yesterday










  • Ok.. another thing: did you mean the flux through the boundary of D? Because when formulating such a question, one needs to specify the surface exactly.
    – zokomoko
    yesterday











  • yes out of the boundary
    – NPLS
    yesterday












up vote
0
down vote

favorite









up vote
0
down vote

favorite











$D=x^2+y^2+z^2le 8,zge 2F=0,0,z^2/2$



In order to find the flux (out of the boundary of $D$) I used the divergence theorem $div=z$.



Is the flux:



$int_theta=0^theta=2piint_z=2^z=sqrt8int_r=0^r=sqrt8-z^2zrdrdzdtheta = 4pi$



?




integration multivariable-calculus




share|cite|improve this question













$D=x^2+y^2+z^2le 8,zge 2F=0,0,z^2/2$



In order to find the flux (out of the boundary of $D$) I used the divergence theorem $div=z$.



Is the flux:



$int_theta=0^theta=2piint_z=2^z=sqrt8int_r=0^r=sqrt8-z^2zrdrdzdtheta = 4pi$



?





integration multivariable-calculus





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited yesterday
























asked yesterday









NPLS

1819




1819











  • You forgot to multiply by the Jacobian
    – zokomoko
    yesterday










  • forgot to write it, but I did calculation with it
    – NPLS
    yesterday











  • @NPLS: So please include the Jacobian in your problem statement so that others are not confused.
    – David G. Stork
    yesterday










  • Ok.. another thing: did you mean the flux through the boundary of D? Because when formulating such a question, one needs to specify the surface exactly.
    – zokomoko
    yesterday











  • yes out of the boundary
    – NPLS
    yesterday
















  • You forgot to multiply by the Jacobian
    – zokomoko
    yesterday










  • forgot to write it, but I did calculation with it
    – NPLS
    yesterday











  • @NPLS: So please include the Jacobian in your problem statement so that others are not confused.
    – David G. Stork
    yesterday










  • Ok.. another thing: did you mean the flux through the boundary of D? Because when formulating such a question, one needs to specify the surface exactly.
    – zokomoko
    yesterday











  • yes out of the boundary
    – NPLS
    yesterday















You forgot to multiply by the Jacobian
– zokomoko
yesterday




You forgot to multiply by the Jacobian
– zokomoko
yesterday












forgot to write it, but I did calculation with it
– NPLS
yesterday





forgot to write it, but I did calculation with it
– NPLS
yesterday













@NPLS: So please include the Jacobian in your problem statement so that others are not confused.
– David G. Stork
yesterday




@NPLS: So please include the Jacobian in your problem statement so that others are not confused.
– David G. Stork
yesterday












Ok.. another thing: did you mean the flux through the boundary of D? Because when formulating such a question, one needs to specify the surface exactly.
– zokomoko
yesterday





Ok.. another thing: did you mean the flux through the boundary of D? Because when formulating such a question, one needs to specify the surface exactly.
– zokomoko
yesterday













yes out of the boundary
– NPLS
yesterday




yes out of the boundary
– NPLS
yesterday















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