return the integral of a function defined over a region - Maple Help

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Student[MultivariateCalculus][MultiInt] - return the integral of a function defined over a region

Calling Sequence

MultiInt(f(x,y), x=a..b, y=c..d, opts)

MultiInt(f(x,y,z), x=a..b, y=c..d, z=e..f, opts)

Parameters

f(x, y), f(x, y, z)

-

algebraic expressions

x, y, z

-

name; specify the independent variables

a, b, c, d, e, f

-

algebraic; limits of integration

opts

-

(optional) equation(s) of the form option=value where option is coordinates or output; specify output options

Description

• 

The MultiInt command returns the integral of a function over a region in space.

• 

The opts argument can contain any of the following equations that set output options.

  

 

  

coordinates = cartesian[x,y], polar[r,theta] (2-D), cartesian[x,y,z], cylindrical[r,theta,z], spherical[r,phi,theta]

  

Determines the coordinate system being used. The first variable of polar, cylindrical, and spherical is assumed to be the radial component. The default is cartesian.

  

 

  

output = value, integral or steps

  

This option controls the return value of the function.

  

* output = value specifies that the value of the integral is returned. The default is output = value.

  

* output = integral specifies that the inert form of the integral is shown.

  

* output = steps specifies that the intermediate steps of solving the multiple integral are shown.

Examples

withStudent[MultivariateCalculus]:

MultiInt3x2+3y2,x=1..4,y=1..6

1092

(1)

MultiIntr,r=1..4,θ=0..π2,coordinates=polarr,θ

212π

(2)

MultiIntr+θ+z,r=0..2,θ=2..4,z=π2..π,coordinates=cylindricalr,θ,z

263π+32π2

(3)

MultiIntr,r=0..π,θ=0..π,φ=0..π,coordinates=sphericalr,θ,φ

12π5

(4)

MultiIntx2+y2+z,z=2..4+y2,y=x1..x+6,x=2..4,output=integral

∫24∫x1x+6∫2y2+4x2+y2+zⅆzⅆyⅆx

(5)

See Also

Student, Student[MultivariateCalculus]


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