and why is it 0? what does the integrand not being defined at (0,0) has to do with that? by a cut do u mean to make a line connecting the 2 ellipses? could u explain more please?
checked it and still got the same. is it allowed to say 9x^2 + 16y^2 = 144 on that integral? that's something I'm using.
for ii, if u could mention some of the methods u have in mind, i might recognize it as something given in class. thnx
got pi/6 for i. didn't use green's for that. the other way is easier. for ii u can't use green's since it would either be too complicated or impossible to integrate. yes i know green's thm. sorry for not showing any work. i just don't know what to do for ii.
Homework Statement
(i) Evaluate
\int_C \dfrac{-ydx + xdy}{9x^2 + 16y^2}
when C is the ellipse
\dfrac{x^2}{16} + \dfrac{y^2}{9} = 1
(ii) Use the ans to (i) to evaluate the integral along C' = ellipse:
\dfrac{x^2}{25} + \dfrac{y^2}{16} = 1
Homework Equations
The...
Homework Statement
find the area bounded by one of the four loops of: (x^2 + y^2)^3 = 4x^2y^2
Homework Equations
The Attempt at a Solution
I converted to polar coordinates and got r^{3/2} = sin^2(2\theta)
The typical formula for polar integration for area would imply that I...
Can we just say that if F has characteristic p, then |G| = p - 1. Since G is cyclic then it isomorphic to Z*_p (which is also cyclic), and then use Wilson's Theorem and the isomorphism to conclude the product is -1.
Homework Statement
Let F be a finite field. Show that the product of all non-zero elements of F is -1.
Homework Equations
An example of this is Wilson's Theorem.
The Attempt at a Solution
Let G be the multiplicative group of non-zero elements of F. Then G is cyclic. Let a...