The transformation x=au , y=bv (a>0,b>0) can be rewritten as x/a=u,y/b=v , and hence it maps the circular region u2+v2≤c into the elliptical region x2a2+y2b2≤c Let R be the region x^2/25+y^2/25≤20 .
Transform the integral over R into an integral over a circular region. ∫∫Re^−(25x2+25y2) dA=∫BA∫DCF(u,v)dudv where A= ? , B= ? , C= ? , D= ? , F(u,v)= ?.
After the change of variables this integral is simple if done the right way. In particular we obtain ∫∫Re^−(25x2+25y2)dA= ?
