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## Homework Statement

F=<0,3,x^2> computer the surface integral over the hemisphere x^2 + y^2 + z^2 = 9

z greater than or equal to 0, outward pointing normal.

## Homework Equations

## The Attempt at a Solution

I don't know why I keep getting this problem wrong. The general formula for surface integrals of vector fields is [tex]\int[/tex][tex]\int[/tex]F([tex]\Phi[/tex]([tex]\theta[/tex],[tex]\phi[/tex])*(dot product) n([tex]\theta[/tex],[tex]\phi[/tex]) For a sphere the normal is defined in the chapter of my text as R^2 sin([tex]\phi[/tex])<cos([tex]\theta[/tex])sin([tex]\phi[/tex]),sin([tex]\theta[/tex])sin([tex]\phi[/tex]),cos([tex]\phi[/tex])> However in the solutions manual when they are setting up the Integral they just have the sin([tex]\phi[/tex])<cos([tex]\theta[/tex])sin([tex]\phi[/tex]),sin([tex]\theta[/tex])sin([tex]\phi[/tex]),cos([tex]\phi[/tex])> but no R^2 ? I was looking over a sample problem on Pauls online notes and he did include the R^2 when setting up the integral so I am a little confused They end up getting 9pi/4. Can anyone help this isn't a homework problem I am just studying for my final which is in a few days thanks a lot.