In mathematics — in particular, in multivariable calculus — a volume integral refers to an integral over a 3-dimensional domain.
A volume integral is a triple integral of the constant function 1, which gives the volume of the region D. That is, the integral
It can also mean a triple integral within a region D in R3 of a function and is usually written as:
A volume integral in cylindrical coordinates is
and a volume integral in spherical coordinates (using the standard convention for angles, i.e. with φ as the azimuth) has the form
Read more about Volume Integral: Example
Famous quotes containing the words volume and/or integral:
“We are too civil to books. For a few golden sentences we will turn over and actually read a volume of four or five hundred pages.”
—Ralph Waldo Emerson (1803–1882)
“Make the most of your regrets; never smother your sorrow, but tend and cherish it till it come to have a separate and integral interest. To regret deeply is to live afresh.”
—Henry David Thoreau (1817–1862)