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Iterated Triple Integral in Cylindrical Coordinates
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Description
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Compute the iterated triple integral in cylindrical coordinates.
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Iterated Triple Integral in Cylindrical Coordinates
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Integrand:
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>
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| (1) |
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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=3972/file05543/math66.png)
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](/support/helpjp/helpview.aspx?si=3972/file05543/math73.png)
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| (2) |
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](/support/helpjp/helpview.aspx?si=3972/file05543/math89.png)
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| (3) |
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](/support/helpjp/helpview.aspx?si=3972/file05543/math105.png)
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| (4) |
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](/support/helpjp/helpview.aspx?si=3972/file05543/math121.png)
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| (5) |
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| (6) |
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| (7) |
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Inert Integral: 
(Note automatic insertion of Jacobian.)
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![Student[MultivariateCalculus][MultiInt](__z__, __z__ = __r__ .. 1, __r__ = 0 .. 1, theta = 0 .. 2*Pi, coordinates = cylindrical[__r__, theta, __z__], output = integral)](/support/helpjp/helpview.aspx?si=3972/file05543/math186.png)
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| (8) |
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Value:
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![Student[MultivariateCalculus][MultiInt](__z__, __z__ = __r__ .. 1, __r__ = 0 .. 1, theta = 0 .. 2*Pi, coordinates = cylindrical[__r__, theta, __z__])](/support/helpjp/helpview.aspx?si=3972/file05543/math202.png)
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| (9) |
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Stepwise Evaluation:
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![Student[MultivariateCalculus][MultiInt](__z__, z = __r__ .. 1, r = 0 .. 1, theta = 0 .. 2*Pi, coordinates = cylindrical[r, theta, z], output = steps)](/support/helpjp/helpview.aspx?si=3972/file05543/math218.png)
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| (10) |
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