September 12th, 2017, 09:50 PM  #1 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 876 Thanks: 60 Math Focus: सामान्य गणित  Volume integration
$\displaystyle F=(2x^{2}3z)i2xy4xk$ Evaluate volume integration of $\displaystyle \bigtriangledown \cdot F$ over a vloume bounded by the planes $\displaystyle x=0$, $\displaystyle y=0$, $\displaystyle z=0$ and $\displaystyle 2x+3y+z =4$ I got answer as $\displaystyle 16/9$, is it correct? Last edited by MATHEMATICIAN; September 12th, 2017 at 09:54 PM. 
September 12th, 2017, 10:04 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,781 Thanks: 919 
should this be $F=(2x^2  3z)\hat{i}  2xy \hat{j}  4x \hat{k}$ ? 
September 12th, 2017, 10:06 PM  #3 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 876 Thanks: 60 Math Focus: सामान्य गणित  
September 12th, 2017, 10:10 PM  #4 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 876 Thanks: 60 Math Focus: सामान्य गणित  
September 12th, 2017, 10:20 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 1,781 Thanks: 919  
September 12th, 2017, 10:22 PM  #6 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 876 Thanks: 60 Math Focus: सामान्य गणित  
September 12th, 2017, 10:31 PM  #7 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 876 Thanks: 60 Math Focus: सामान्य गणित 
Romsek What is the physical meaning of volume integration of divergence of a vector function? 
September 12th, 2017, 10:58 PM  #8  
Senior Member Joined: Sep 2015 From: USA Posts: 1,781 Thanks: 919  Quote:
Roughly the divergence of a field produces a "charge" density, and the volume integral of this "charge" density is equal to the surface integral of the field through the boundary surface of the volume. I put "charge" in quotes because it can be any sort of field, not just an electric field.  

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