- #1
SigmaCrisis
- 15
- 0
Calculating line integrals...
Ok, the problem is:
h(x,y) = 3x (x^2 + y^4)^1/2 i + 6y^3 (x^2 + y^4)^1/2 j;
over the arc: y = -(1 - x^2)^1/2 from (-1,0) to (1,0).
In my notes, I had written: if h is a gradient, then the INTEGRAL of g*dr over curve C depends only on the endpoints. Also, if the curve C is closed AND h is a gradient, then the integral of g*dr over curve c is 0.
So, my question is, when testing to see if a given function like the one above, should you just test to see if:
partial derivative of the i component with respect to y EQUALS the partial derivative of the j component with respect to x?
If not equal, then it is not a gradient, right?
Thanks.
Ok, the problem is:
h(x,y) = 3x (x^2 + y^4)^1/2 i + 6y^3 (x^2 + y^4)^1/2 j;
over the arc: y = -(1 - x^2)^1/2 from (-1,0) to (1,0).
In my notes, I had written: if h is a gradient, then the INTEGRAL of g*dr over curve C depends only on the endpoints. Also, if the curve C is closed AND h is a gradient, then the integral of g*dr over curve c is 0.
So, my question is, when testing to see if a given function like the one above, should you just test to see if:
partial derivative of the i component with respect to y EQUALS the partial derivative of the j component with respect to x?
If not equal, then it is not a gradient, right?
Thanks.