Student[MultivariateCalculus][ApproximateInt] - return the approximate integral of a bivariate function
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Calling Sequence
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ApproximateInt(f(x,y), x=a..b, y=c..d, z=e..f, opts)
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Parameters
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f(x, y)
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algebraic expression
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x, y
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name; independent variables
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a, b, c, d
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realcons; limits of integration
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z=e..f
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(optional) range over which to plot the dependent variable; e,f are real constants
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opts
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(optional) equation(s) of the form option=value where option is one of coordinates, frames, functionoptions, method, output, partition, prismoptions or showfunction; specify output options
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Description
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The ApproximateInt(f(x,y),x=a..b,y=c..d) calling sequence returns an approximation to the integral of .
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The opts argument can contain any of the following equations that set output options.
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coordinates = cartesian or polar
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Determines whether the integral is calculated in cartesian or polar coordinates. In polar coordinates, the first variable is assumed to be the radial component. The default is cartesian.
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For example, frames = a..b.
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Specifies the number of frames in the animation, b-a+1. Each frame of the animation partitions the plot according to the number in the range a..b corresponding to the current frame. The first frame partitions the domain into an a x a grid. The last frame partitions the domain into a b x b grid. This option is ignored unless output = animation. The default is .
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Specifies the plot options for plotting the function . For more information on plotting options, see plot3d/options.
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method = midpoint, upper, lower, or random
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Calculates the approximation of the integral using the midpoint, upper, lower, or random point Riemann sum. The default is midpoint.
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output = value, plot, or animation
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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 approximation is returned. Plot options are ignored if output = value. The default is output=value.
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* output = plot specifies that a plot displays, which shows the expression and an approximation to the integral.
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* output = animation specifies that an animation displays, which shows the expression and approximations using a sequence of partitions each of which is a refinement of its predecessor.
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partition = [posint, posint]
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The partition option controls the partition of the interval. By default, the interval is partitioned by .
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Specifies the plot options for plotting the approximation to the integral of . For more information on plotting options, see plot3d/options.
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showfunction = true or false
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Determines whether the function is plotted. The default is true.
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The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption , see plot/typesetting.
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Examples
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>
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>
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The command to create the plot from the Plotting Guide is
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