Evaluating 3D Integral in Rectangular Coordinates

[Ions]

Problem: Evaluate (leave in rectangular coordinates):
$$<br /> \int_{-1}^{{1}}}\int_{-{\sqrt{1-x^2}}}^{{\sqrt{1-x^2}}}\int_{-{\sqrt{1-x^2-y^2}}}^{{\sqrt{1-x^2-y^2}}}\ \,dz\,dy\,dx$$

 

[n!kofeyn]

Well, start slow. Can you evaluate this integral?
$$\int_{-{\sqrt{1-x^2-y^2}}}^{{\sqrt{1-x^2-y^2}}}\ \,dz$$

 

[Ions]

$$<br /> 2\int_{-1}^{{1}}}\int_{-{\sqrt{1-x^2}}}^{{\sqrt{1-x^2}}}\2{\sqrt{1-x^2-y^2}}}\,dy\,dx$$

Supposedly it's easier to make a subtitution u = 1-x^2 at this point but I don't see how...