Volume Integral Calculator
Calculate triple integrals over 3D regions using numerical integration.
Function f(x, y, z)
Use: x, y, z, ^, sin, cos, tan, exp, log, sqrt, pi
Integration Bounds
Total evaluations: 8,000
Volume Integral
1.000000
integral integral integral f dV
VRegion Volume
1.000000
avgAverage Value
1.000000
minMin Value
1.000000
maxMax Value
1.000000
Integration Region
x range[0, 1]
y range[0, 1]
z range[0, 1]
Mean Value Theorem
The average value of f over the region equals the integral divided by the volume: f_avg = (1/V) integral f dV = 1.000000
About Volume Integrals
Definition
A volume integral (triple integral) extends integration to three dimensions. It computes the total of a function over a 3D region by summing infinitesimal contributions.
Applications
- Mass of 3D objects with varying density
- Center of mass calculations
- Moments of inertia
- Electric charge in a region