Home

Triple Integral Calculator

Compute a triple integral over a box by 3D Simpson.

展开更多 ▾
∭_V f(x,y,z) dV
e.g. x*y*z

📖 Tutorial | Triple Integral

1. Definition
A triple integral over a box reduces to three iterated integrals. With f=1 it gives the volume.
2. Symbols
fintegrand
Vregion
six boundsbox limits
3. How it works
  • 3D composite Simpson;
  • 16³ weighted grid;
  • f=1 yields the box volume.
4. Steps
  1. Enter f(x,y,z);
  2. Enter six bounds;
  3. Click Calculate.
5. Example
Example: ∭₀¹ xyz dV = (1/2)³=0.125.
6. Pitfalls
This tool supports boxes only;
Other regions need variable limits;
Cylindrical/spherical coords need Jacobians.

❓ FAQ | Triple Integral

Geometric meaning?
Volume when f=1, mass otherwise.
Non-box region?
Set up iterated integrals with variable limits.
Cylindrical Jacobian?
r dr dθ dz.
Spherical Jacobian?
ρ² sinφ dρ dφ dθ.
Small error?
Limited 3D resolution.