Question

evaluate the integral $$\int_R\int xy dx dy$$ over the region R covered by $$\frac{x^2}{a^2}+\frac{y^2}{b^2}= 1$$
in the first quadrant

Answer 1

\[\int\limits_{x = 0}^{a}\int\limits_{y = 0}^{ +b \sqrt { \left (1 - \frac{x^2}{a^2} \right )}} xy \ dy \ dx\]

Answer 2

you can param it too, but this is a pretty easy integral

Answer 3

Thank you!!...struggled to find limits. :)

Answer 4

and this works too...
\[\int\limits_{y =0}^{b} \int\limits_{x = 0}^{+a \sqrt{ 1 - \frac{y^2}{b^2} }} x \ y \ dx \ dy\]