Hyper-volume by integration - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: Hyper-volume by integration (/showthread.php?tid=1164) Hyper-volume by integration - Xorter - 04/08/2017 Hi, everyone! My dream is to get a formula to get the n-dimensional hyper-volume of an n-dimensional function in cartesian AND polar coordinates, too! So the length of f(x), the area of f(x,y), the volume of f(x,y,z) ... etc. According to the other existing formulas I have created an own in cartesian coordinate system: $V_N = \int ... \int_{V_N} \sqrt{1+\sum_{k=1}^N {}{df \over dx_k}} dx_1 ... dx_N$ 1st question: Do you find it correct? 2nd: How could it look in polar coordinate system? (My final goal is to use these formulas to determine a few things about the base units of the hyperdimensional and interdimensional spaces from its derivatives and its existences. But for it, I need these formulas!)