Formula:141

Digital Library of Mathematical Functions ID 1.5.E43

${\displaystyle{\displaystyle\iiint_{D}f(x,y,z)\mathrm{d}x\mathrm{d}y\mathrm{d}z=\iiint_{D^{*}}f(x(u,v,w),y(u,v,w),z(u,v,w))\*\left|\frac{\partial(x,y,z)}{\partial(u,v,w)}\right|\mathrm{d}u\mathrm{d}v\mathrm{d}w.}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle w}}$: variable
 

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