Find the volume of the region inside the surface $z = x^2 + y^2$ and between $z = 0$ and $z = 10$.
Really the only thing I need help with in this problem is setting up the limits of integration.
$0 = x^2 ---> x = 0$ (lower limit)
$10 = x^2 ---> x = sqrt(10)$ (upper limit)
$0 = x^2 + y^2 ---> y = sqrt(10-x^2)$ (upper limit)
$0 < x < sqrt(10)$
$0 < y < sqrt(10-x^2)$
then it should be the double integral of $x^2 + y^2$ with those limits dydx.
However, when I calculate this, my answer ends up negative. Did I mess up the integral or the limits?