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Average Value of a Function in Polar Coordinates
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Description
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In the polar coordinate system, where the point  has coordinates  , determine the average value of a function.
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Average Value of a Function in Polar Coordinates
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Integrand
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| (1) |
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Region:  <= r and r <= r[2](theta)}](/support/helpjp/helpview.aspx?si=3993/file05337/math71.png)
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](/support/helpjp/helpview.aspx?si=3993/file05337/math78.png)
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| (2) |
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](/support/helpjp/helpview.aspx?si=3993/file05337/math94.png)
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| (3) |
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| (4) |
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| (5) |
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Inert Integral: 
(Note automatic insertion of Jacobian.)
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![Student[MultivariateCalculus][FunctionAverage](theta/(1+r^2), r = 0 .. theta, theta = 0 .. (1/3)*Pi, coordinates = polar[r, theta], output = integral)](/support/helpjp/helpview.aspx?si=3993/file05337/math160.png)
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| (6) |
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Value
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![Student[MultivariateCalculus][FunctionAverage](theta/(1+r^2), r = 0 .. theta, theta = 0 .. (1/3)*Pi, coordinates = polar[r, theta])](/support/helpjp/helpview.aspx?si=3993/file05337/math176.png)
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| (7) |
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