September 12th, 2017, 09:50 PM  #1 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 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: 2,505 Thanks: 1374 
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: 901 Thanks: 61 Math Focus: सामान्य गणित  
September 12th, 2017, 10:10 PM  #4 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 Math Focus: सामान्य गणित  
September 12th, 2017, 10:20 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 2,505 Thanks: 1374  
September 12th, 2017, 10:22 PM  #6 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 Math Focus: सामान्य गणित  
September 12th, 2017, 10:31 PM  #7 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 901 Thanks: 61 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: 2,505 Thanks: 1374  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.  

Tags 
integration, volume 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Volume integration  MATHEMATICIAN  PreCalculus  13  September 2nd, 2017 09:21 PM 
Volume integration  MATHEMATICIAN  Calculus  13  September 1st, 2017 11:12 AM 
integration of volume  xl5899  Calculus  2  December 10th, 2015 09:09 AM 
Application of integration. (Volume)  jiasyuen  Calculus  9  March 29th, 2015 08:37 PM 
integration and volume?  izseekzu  Calculus  1  January 26th, 2010 06:34 PM 