Each triple integral calculates the volume of one of the solids pictured below. Match each integral with the label A - E of its corresponding solid. As always, you may click on the thumbnail image to produce a larger image in a new window. Just take your time; a process of elimination will help with matches that are not obvious.

1. $\displaystyle \int_{-1}^1\int_{-\sqrt{1-{x^2}}}^{\sqrt{1-{x^2}}}\int_{-\sqrt{1-{x^2}-y^2}}^{\sqrt{1-{x^2}-y^2}}dzdydx$

2. $\displaystyle \int_{-\sqrt{2}}^{\sqrt{2}}\int_{-\sqrt{\sqrt{2}-x^2}}^{\sqrt{\sqrt{2}-x^2}}\int_{x^2+y^2}^{4-x^2-y^2}dzdydx$

3. $\displaystyle \int_{-2}^2\int_{-\sqrt{1-\frac{x^2}{2}}}^{\sqrt{1-\frac{x^2}{2}}}\int_{-\sqrt{1-\frac{x^2}{2}-y^2}}^{\sqrt{1-\frac{x^2}{2}-y^2}}dzdydx$

4. $\displaystyle \int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{0}^{6-x-3y}dzdydx$

5. $\displaystyle \int_{-1}^1\int_{-\sqrt{1-x^2}}^{\sqrt{1-x^2}}\int_{-\sqrt{1-x^2-y^2}-1}^{\sqrt{1-x^2-y^2}+1}dzdydx$

A B C D E     Your overall score for this problem is