Average and Integral
Select an Average () or Integral () data set, found under the More Data Sets submenu, to compute the average or integral of another data set, for example, to plot the average or integral.
Data
Select a Data set for the data to compute the average or integral. To compute the average or integral for a Solution data set, use a Selection to define the geometric entity (point, boundary, edge, or domain) to integrate over. Right-click the data set and select Add Selection.
Settings
Select an integration Method: Auto (the default), Integration, or Summation.
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Auto — Computes the integral for fields by numerical integration and for reaction forces by summation. Predefined quantities for reaction forces use summation instead of integration. Also, to specify an expression for the integrand, use the reacf operator, and the automatic setting chooses the summation method.
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Integration — the standard numerical integration method (quadrature).
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 Summation — a summation method useful for computing reaction forces. The summation method finds all nodes on the boundary, evaluates the expression in the nodes and sums up the values. Reaction force variables are predefined in the structural mechanics interfaces. This is selected instead of Integration for reaction forces when the automatic selection of integration method is active.
For Integration order, the COMSOL Multiphysics software determines an appropriate integration order for the expression when you use integration. The default is 4. Select the check box to make a different entry in the field (as an integer that is 0 or larger). COMSOL Multiphysics then performs the integration elementwise using numeric quadrature of the selected order.
Select a Geometry level — Take from data set (the default), Volume, Surface, Line, or Point. The default means the highest geometry dimension for the data in the data set; typically volumes in 3D, surfaces in 2D, and lines in 1D.
If the data set represents data for a 1D or 2D axisymmetric geometry, the Compute surface integral (1D axial symmetry) and Compute volume integral (2D axial symmetry) check boxes are selected by default to compute an average or integral that takes the axial symmetry into account. COMSOL Multiphysics then multiplies the expression (integrand) with 2*pi*r prior to integration to compute the corresponding volume or surface integral.
For an integral evaluation data set example see Flow Past a Cylinder: Application Library path COMSOL_Multiphysics/Fluid_Dynamics/cylinder_flow.