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Average Value of a Function in Cylindrical Coordinates
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Description
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In the cylindrical coordinate system, where the point  has coordinates  , and
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 are the polar coordinates of  , determine the average value of a function.
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Average Value of a Function in Cylindrical Coordinates
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Integrand
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Region:  <= r and r <= r[2](theta), z[1](r, theta) <= z and z <= z[2](r, theta)}](/support/helpjp/helpview.aspx?si=3992/file05336/math79.png)
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](/support/helpjp/helpview.aspx?si=3992/file05336/math86.png)
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](/support/helpjp/helpview.aspx?si=3992/file05336/math102.png)
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](/support/helpjp/helpview.aspx?si=3992/file05336/math118.png)
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](/support/helpjp/helpview.aspx?si=3992/file05336/math134.png)
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Inert Integral: 
(Note automatic insertion of Jacobian.)
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![Student[MultivariateCalculus][FunctionAverage](z, z = r .. 1, r = 0 .. 1, theta = 0 .. 2*Pi, coordinates = cylindrical[r, theta, z], output = integral)](/support/helpjp/helpview.aspx?si=3992/file05336/math200.png)
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Value
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![Student[MultivariateCalculus][FunctionAverage](z, z = r .. 1, r = 0 .. 1, theta = 0 .. 2*Pi, coordinates = cylindrical[r, theta, z])](/support/helpjp/helpview.aspx?si=3992/file05336/math216.png)
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