# Math Help - Green's theorem

1. ## Green's theorem

Mods | Mathematical Institute - University of Oxford

paper D, 2008
question 4b

I really cant see where to start, but I guess it's a fairly standard Green's theorem result.. the squares are putting me off alot

could someone please show me how to do it.

many thanks

2. Originally Posted by James0502
Mods | Mathematical Institute - University of Oxford

paper D, 2008
question 4b

I really cant see where to start, but I guess it's a fairly standard Green's theorem result.. the squares are putting me off alot

could someone please show me how to do it.

many thanks
Using Green's theorem you want to calculate

$\frac{1}{2}\int_0^{2\pi} x dy - y dx$ where

$x = 4 \cos \phi - \cos 4 \phi,\;\;y = 4 \sin \phi - \sin 4 \phi$

3. Note $x dy - y dx$ simplifies very nicely!

4. sorry.. I still dont understand.. How have they found the first result for example?

the 'show that' bit...

with (dT/dx)^2 + (dT/dy)^2

many thanks
and what is an epicycloid?

what is the standard result for finding the area of it?