# Math Help - Need help setting this integral.

1. ## Need help setting this integral.

Solid bounded above by z=2-x^2-y^2 and below by z=x^2+y^2.

2. $\int\int\int_S dzdydx$

$z_1 = 2-x^2 -y^2$ , $z_2 = x^2 +y^2$

$z_1 = z_2$

$2-x^2 -y^2 = x^2 +y^2 \Rightarrow x^2 +y^2 =1$

z change from $z_2$ to $z_1$

$\int_{-1}^{1} \int_{-\sqrt{1-y^2}}^{\sqrt{1-y^2}} \int_{x^2+y^2}^{2-x^2-y^2} dz dx dy$

3. Can you do it in cylindrical coordinates?

4. $\int_{0}^{2\pi}\int_{0}^{1}\int_{r^2}^{2-r^2} r dzdrd\theta$