- #1
wahaj
- 156
- 2
I was looking at an example where it was evaluating a closed loop integral of a vector field around a triangle (0,0) (1,1) (2,0) by using greens theorem. This example was in the green's theorem section of the book so green's theorem must be used. Anyways the double integral was set up as follows
[tex]\int \int_T (y+x) dA [/tex]
This integral wasn't evaluated the way I have been taught before but rather the book used the following formula
[tex] (\bar{y}+\bar{x}) \times area \ of \ triangle [/tex]
In another instance a closed loop integrals of a vector field around F was evaluated and the formula used there was
(area of circle) ∇F [itex]\bullet[/itex] [itex]\widehat{n}[/itex]
I have never seen these formulas before and the book offers no explanation. Where does this formula come from?
On a side note does green's theorem evaluate the closed loop integral in the counterclockwise direction?
[tex]\int \int_T (y+x) dA [/tex]
This integral wasn't evaluated the way I have been taught before but rather the book used the following formula
[tex] (\bar{y}+\bar{x}) \times area \ of \ triangle [/tex]
In another instance a closed loop integrals of a vector field around F was evaluated and the formula used there was
(area of circle) ∇F [itex]\bullet[/itex] [itex]\widehat{n}[/itex]
I have never seen these formulas before and the book offers no explanation. Where does this formula come from?
On a side note does green's theorem evaluate the closed loop integral in the counterclockwise direction?