Volume in calculus::Volume

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Volume in calculus In calculus, a branch of mathematics, the volume of a region D in R3 is given by a triple integral of the constant function $f(x,y,z)=1$ and is usually written as:

$\iiint\limits_D 1 \,dx\,dy\,dz.$

The volume integral in cylindrical coordinates is

$\iiint\limits_D r\,dr\,d\theta\,dz,$

and the volume integral in spherical coordinates (using the convention for angles with $\theta$ as the azimuth and $\phi$ measured from the polar axis (see more on conventions)) has the form

$\iiint\limits_D \rho^2 \sin\phi \,d\rho \,d\theta\, d\phi .$

Volume sections
Intro  Units   Related terms    Volume in calculus    Volume formulas    Volume formula derivations    Volume in differential geometry    Volume in thermodynamics    See also   References  External links

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