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 xi are functions of s and t.

Area[{x1,,xn},{s,smin,smax},{t,tmin,tmax},chart]

interprets the xi as coordinates in the specified coordinate chart.

Details 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 {s,t,x}.
• Coordinate charts in the fourth argument of Area can be specified as triples {coordsys,metric,dim} in the same way as in the first argument of CoordinateChartData. The short form in which dim is omitted may be used.
• The following options can be given:
•  Assumptions \$Assumptions assumptions to make about parameters Method Automatic method to use WorkingPrecision Infinity the precision used in internal computations
• Specific methods include:
•  Automatic automatic 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 "ParameterRangeAssumptions" property of CoordinateChartData.

Examples

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Basic Examples(5)

The area of a disk:

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The surface area of a sphere:

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The area of an annulus with inner radius 1 and outer radius 2:

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The 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 0:

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

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