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## Homework Statement

calculating volume under a surface, defined by implicit function f(x, y, z)=0 (in cartesian coordinates, strictly not in polar). Because the function that i need to integrate is quite complicated and there would be no obvious way to double check the result i first tried to calculate volume under sphere, but i get the wrong result.

## Homework Equations

so let it be [tex]f(x, y, z)=x^2+y^2+z^2-1[/tex]

## The Attempt at a Solution

[tex]V=8*\int dxdydz[/tex]

where dz is integrated from 0 to [tex]\sqrt{1-x^2-y^2}[/tex], dy from 0 to 1 and the same with dx. The multiplication factor 8 is added to get the whole volume.

I use Mathematica for solving the equation and get [tex]\frac{2}{3}(2\pi - i*(-4 + \log{16}))[/tex]

what am I doing wrong?