Volume Integration, Surface Integration, and Line Integration
The derived integration values are useful for calculating integrated quantities for each solution in a dataset (a time-dependent solution, for example). Also apply an average, maximum, or other operation to compute the average of an integrated quantity, for example.
Under Results, right-click Derived Values () or any Evaluation Group node (), and from the Integration submenu select:
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Volume Integration () to evaluate an integral over a set of domains in 3D models. The result of the evaluation is stored in a Table and displayed in the Table window.
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Surface Integration () to evaluate an integral over a set of domains in 2D, 2D axisymmetric, or boundaries in 3D.
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Line Integration () to evaluate an integral over a set of domains in 1D, boundaries in 2D, or edges in 3D. Integrate over any dataset of the right dimension. For example, make a volume integration of a 2D revolved dataset or a surface integration of a cut plane.
Data
In the Data section you define the data for the integration.
From the Dataset list, choose None, From parent (the default), or any applicable dataset.
Depending on the type of data, a Solution parameters list can appear, with the options From parent or Manual. If you choose Manual, then other lists, such a s Parameter selection and Time selection, will be available for choosing solution parameters to include in the integration.
Also, in datasets from models that contain parametric sweeps, a Table columns list is available for choosing table columns to include:
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 Data only (the default)
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 Inner solutions (such as time steps)
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 Outer solutions (such as the parametric solutions)
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The parameter names in the sweep
Go to Common Results Node Settings for information about these sections: Selection, Through-Thickness Location, Expressions, Integration Settings, and Data Series Operation.
For volume integration examples, and if you have the:
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AC/DC Module, for both a volume and surface integration example, see Eddy Currents: Application Library path ACDC_Module/Introductory_Electromagnetics/eddy_currents.
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RF Module, see Microwave Oven: Application Library path RF_Module/Microwave_Heating/microwave_oven.
For a surface integration example see Effective Diffusivity in Porous Materials: Application Library path COMSOL_Multiphysics/Diffusion/effective_diffusivity.
For line integration examples, and if you have the:
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AC/DC Module, see An RFID System: Application Library path ACDC_Module/Introductory_Magnetostatics/rfid.
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CFD Module, see Capillary Filling — Level Set Method: Application Library path CFD_Module/Multiphase_Flow/capillary_filling_ls.
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Microfluidics Module, see Capillary Filling — Level Set Method: Application Library path Microfluidics_Module/Two-Phase_Flow/capillary_filling_ls.
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Heat Transfer Module, see Radiation in a Cavity: Application Library path Heat_Transfer_Module/Verification_Examples/cavity_radiation.