john_wilfred
New member
- Joined
- Feb 15, 2016
- Messages
- 1
Hey, I've been needing to do this question using Gauss' theorem for a while now and I'm quite stumped. I fully understand what Gauss' law is and what it's used for, I've done many many questions using it before, however this question is messing with me.
So we have a vector field F(x,y,z) = yi + zj + zk and we want the flux through the region bounded by the planes z = 0, x = 0, y = 0 and x + 2y + 3z = 6. So I thought for the bounds for the triple integral I'd have:
0 < x < 3/2
0 < y < 3 - x/2
0 < z < 2 - 2y/3 - x/3
And the integrand would be 1 because the divergence of F is 1. However when I evaluate this integral I get 111/32, and the answer should be 6. Also I know for sure that it's not a calculation error as I put the integral into Matlab and it gave the same answer. So something is wrong with my bounds/integrand/method overall. Also I'm not interested in finding a solution without using Gauss' theorem, I need to use Gauss' theorem to solve this problem.
So we have a vector field F(x,y,z) = yi + zj + zk and we want the flux through the region bounded by the planes z = 0, x = 0, y = 0 and x + 2y + 3z = 6. So I thought for the bounds for the triple integral I'd have:
0 < x < 3/2
0 < y < 3 - x/2
0 < z < 2 - 2y/3 - x/3
And the integrand would be 1 because the divergence of F is 1. However when I evaluate this integral I get 111/32, and the answer should be 6. Also I know for sure that it's not a calculation error as I put the integral into Matlab and it gave the same answer. So something is wrong with my bounds/integrand/method overall. Also I'm not interested in finding a solution without using Gauss' theorem, I need to use Gauss' theorem to solve this problem.