0
$\begingroup$

$D=\{(x,y)|5x^2+6y^2\leq1\}$

$\int\int_D \frac{x^2}{(5x^2+6y^2)^\frac3 2}$

The integrand is not bounded. When performing a polar transformation for the ellipse domain the integrand becomes bounded since the Jacobean is $\frac{1}{\sqrt40}r$:

$\frac{1}{\sqrt 40} cos^2(\theta)$

I was wondering what is the reason for that and if there is an intuitive way of understanding this transformation.

  • 0
    why is the integrand "not bounded"? – 2017-01-26
  • 0
    I think the integrand is not bounded over the domain since $\frac{x^2}{(5x^2+6y^2)^{3/2}}\leq\frac{1}{5^{3/2}}\frac{1}{|x|}.$ – 2017-01-27

0 Answers 0