A volume integral is an extension of a double or triple integral used to calculate the integral of a scalar or vector field over a volume. Volume integrals have various applications in physics, engineering, and mathematics, such as finding the mass, charge, or density of a three-dimensional object, as well as calculating the total energy, momentum, or force acting on a system.
Volume integrals are typically computed using triple integrals in rectangular, cylindrical, or spherical coordinates. The choice of coordinate system depends on the geometry of the volume and the field being integrated. By dividing the volume into infinitesimally small elements and summing the contributions of each element, a volume integral can be used to calculate the accumulated quantity over the entire volume.