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Student[MultivariateCalculus][MultiInt] - return the integral of a function defined over a region
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Calling Sequence
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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)
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Parameters
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f(x, y), f(x, y, z)
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algebraic expressions
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x, y, z
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name; specify the independent variables
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a, b, c, d, e, f
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algebraic; limits of integration
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opts
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(optional) equation(s) of the form option=value where option is coordinates or output; specify output options
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Description
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The MultiInt command returns the integral of a function over a region in space.
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The opts argument can contain any of the following equations that set output options.
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coordinates = cartesian[x,y], polar[r,theta] (2-D), cartesian[x,y,z], cylindrical[r,theta,z], spherical[r,phi,theta]
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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.
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output = value, integral or steps
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This option controls the return value of the function.
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* output = value specifies that the value of the integral is returned. The default is output = value.
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* output = integral specifies that the inert form of the integral is shown.
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* output = steps specifies that the intermediate steps of solving the multiple integral are shown.
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Examples
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![with(Student[MultivariateCalculus])](/support/helpjp/helpview.aspx?si=4274/file05050/math155.png)
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![MultiInt(r, r = 1 .. 4, theta = 0 .. (1/2)*Pi, coordinates = polar[r, theta])](/support/helpjp/helpview.aspx?si=4274/file05050/math166.png)
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![MultiInt(r+theta+z, r = 0 .. 2, theta = 2 .. 4, z = (1/2)*Pi .. Pi, coordinates = cylindrical[r, theta, z])](/support/helpjp/helpview.aspx?si=4274/file05050/math173.png)
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![MultiInt(r, r = 0 .. Pi, theta = 0 .. Pi, phi = 0 .. Pi, coordinates = spherical[r, theta, phi])](/support/helpjp/helpview.aspx?si=4274/file05050/math180.png)
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| (5) |
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