1. Find the area of the region bounded by x^2 - xy + y^2 = 2:(adsbygoogle = window.adsbygoogle || []).push({});

a)let x = au + bv, y= au - bv therefore, 3b^2v^2 + a^2u^2 = 2

b) Choose a and b such that u^2 + v^2 = 1, therefore, a = sqrt 2 & b = (sqrt 6)/3

c) Applying these results and changing variables into u and v, evaluate the integral //(x^2 - xy + y^2) dxdy, where the integral is bounded by the equation x^2 - xy + y^2 = 2.

For the part c) I have found the J(u,v) = 4(sqrt 3)/3, but in the examples I have I am supposed to follow this up with an integral and I am not sure what to do next. Are there any suggestions?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Long Question

**Physics Forums | Science Articles, Homework Help, Discussion**