- #1
goraemon
- 67
- 4
Homework Statement
The problem is given in the attached file.
Homework Equations
Divergence theorem, flux / surface integral
The Attempt at a Solution
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As you can see I got the question correct using Divergence theorem. But I wanted to make sure that I could arrive at the same answer using the standard method for surface integrals, so I tried the following:
Given S: x+y+z=4, bounded by the axes.
->dS = ##\sqrt3 dx dy##
-> the normal vector = ##\frac{i + j + k}{\sqrt3}##
SO, F * n dS becomes -> (6xy + 2z) + (y^2 + 1) - (x + y) dx dy
= 6xy + 2(4 - x - y) + y^2 + 1 - x - y dx dy
The region's bounds for the double integral is: 0 <= x <= 4, and 0 <= y <= 4 - x.
Solving the double integral gets me 280 / 3...which is inconsistent with the correct answer I got using Divergence Theorem.
Where did I go wrong? And sorry in advance for the less-than-stellar formatting.