Calculate areas of shapes bounded by curves
The expression is given
$\frac{(2x+3y-5)^2}{16} + \frac{(3x-2y+1)^2}{25} = 1$
Wanted through $s = \int \int dxdy$, but somehow the limits are not entirely clear.
I decided to make a replacement $u = 2x+3y-5\\v = 3x-2y+1$
Then expressed
$x = \frac{1}{13}*(2u+3v+7) \\y = \frac{1}{13}*(3u-2v+17)$
Found partial derivatives for Jacobian and found Jacobian
$J = |\frac{1}{13}|$
Then he moved to the polar coordinates $u = 4rcos(\phi)\\ v=5rsin(\phi)$
And after the substitution, everything was reduced to $r = 1$
And now I'm stupid and I don’t know whether to set the limits for the integral or write something else ...
I can’t solve it.