# How can the following integral be evaluated without using Green's Theorem?

How can the following integral be solved without using Green's Theorem and without converting it into a line integral?
$\iint_{R}(-1)dxdy$
where R is the region enclosed by $x=\cos(t)$, $y=2\sin(t)$, and $t$ varies from
$t=0$ to $t=2\pi$

How can the Jacobian be evaluated in this case?

• This is the negative of the area of the ellipse $x^2 + (y/2)^2 = 1$. – Tob Ernack Jul 12 '17 at 11:03