Area

Area[reg]
gives the area of the two-dimensional region reg.

Area[{x1,,xn},{s,smin,smax},{t,tmin,tmax}]
gives the area of the parametrized surface whose Cartesian coordinates are functions of s and t.

Area[{x1,,xn},{s,smin,smax},{t,tmin,tmax},chart]
interprets the as coordinates in the specified coordinate chart.

Details and OptionsDetails and Options

  • Area is also known as surface area.
  • A two-dimensional region can be embedded in any dimension greater than or equal to two.
  • In Area[x,{s,smin,smax},{t,tmin,tmax}], if x is a scalar, Area returns the area of the parametric surface .
  • Coordinate charts in the fourth argument of Area can be specified as triples in the same way as in the first argument of CoordinateChartData. The short form in which dim is omitted may be used.
  • Area takes an Assumptions option that can be used to specify assumptions on parameters.
  • The following options can be given:
  • Assumptions$Assumptionsassumptions to make about parameters
    MethodAutomaticmethod to use
  • Specific methods include:
  • Automaticautomatic method selection
    "Integrate"exact symbolic integration
    "NIntegrate"numeric integration
  • Additional method suboptions can be given in the form Method->{,opts}.
  • Any option of Integrate or NIntegrate can be passed as a method suboption to the corresponding method.
  • Symbolic limits of integration are assumed to be real and ordered. Symbolic coordinate chart parameters are assumed to be in range given by the property of CoordinateChartData.

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

The area of a disk:

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The surface area of a sphere:

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Area of an anulus with inner radius 1 and outer radius 2:

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Surface area of the open cylinder , expressed in cylindrical coordinates:

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The area of a region of dimension zero or one is :

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The area of a region of dimension three or higher is :

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Introduced in 2014
(10.0)