Volume in calculus::Volume


Volume::volume    Center::style    Radius::geometry    Sphere::''h''    Height::cubic    Manifold::integral

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 <math>f(x,y,z)=1</math> and is usually written as:

<math>\iiint\limits_D 1 \,dx\,dy\,dz.</math>

The volume integral in cylindrical coordinates is

<math>\iiint\limits_D r\,dr\,d\theta\,dz, </math>

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

<math>\iiint\limits_D \rho^2 \sin\phi \,d\rho \,d\theta\, d\phi .</math>

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  

Volume in calculus