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Iterated Triple Integral in Spherical Coordinates
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Description
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Compute the iterated triple integral in spherical coordinates.
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Iterated Triple Integral in Spherical Coordinates
( = colatitude, measured down from  -axis)
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Integrand:
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| (1) |
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Region:  <= phi and phi <= phi[2](theta), rho[1](phi, theta) <= rho and rho <= rho[2](phi, theta)}](/support/helpjp/helpview.aspx?si=3974/file05544/math72.png)
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](/support/helpjp/helpview.aspx?si=3974/file05544/math79.png)
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| (2) |
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](/support/helpjp/helpview.aspx?si=3974/file05544/math95.png)
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| (3) |
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](/support/helpjp/helpview.aspx?si=3974/file05544/math111.png)
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| (4) |
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](/support/helpjp/helpview.aspx?si=3974/file05544/math127.png)
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| (5) |
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| (6) |
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| (7) |
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Inert Integral: 
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![Student[MultivariateCalculus][MultiInt](rho, rho = 0 .. 1, phi = 0 .. (1/6)*Pi, theta = 0 .. 2*Pi, coordinates = spherical[rho, phi, theta], output = integral)](/support/helpjp/helpview.aspx?si=3974/file05544/math182.png)
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| (8) |
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Value:
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![Student[MultivariateCalculus][MultiInt](rho, rho = 0 .. 1, phi = 0 .. (1/6)*Pi, theta = 0 .. 2*Pi, coordinates = spherical[rho, phi, theta])](/support/helpjp/helpview.aspx?si=3974/file05544/math198.png)
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| (9) |
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Stepwise Evaluation:
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![Student[MultivariateCalculus][MultiInt](rho, rho = 0 .. 1, phi = 0 .. (1/6)*Pi, theta = 0 .. 2*Pi, coordinates = spherical[rho, phi, theta], output = steps)](/support/helpjp/helpview.aspx?si=3974/file05544/math214.png)
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| (10) |
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