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 October 15th, 2017, 11:07 AM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 Spherical Challenge.... An object occupies the region in the first octant bounded by the cones $\displaystyle \phi = \frac { \pi }{4}$ and $\displaystyle \phi = arctan 2$, and the sphere $\displaystyle \rho = \sqrt {6}$, and has density proportional to the distance from the origin. Find the mass. is the following correct? $\displaystyle \int_{0}^{ \frac { \pi } {2} } \int_{ \frac { \pi } {4} }^{arctan(2)} \int_{0}^{ \sqrt{6} } \rho ~ \rho^2 sin \phi ~d \rho ~d \phi ~d \theta$ October 15th, 2017, 11:27 AM   #2
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 Originally Posted by zollen An object occupies the region in the first octant bounded by the cones $\displaystyle \phi = \frac { \pi }{4}$ and $\displaystyle \phi = arctan 2$, and the sphere $\displaystyle \rho = \sqrt {6}$, and has density proportional to the distance from the origin. Find the mass. is the following correct? $\displaystyle \int_{0}^{ \frac { \pi } {2} } \int_{ \frac { \pi } {4} }^{arctan(2)} \int_{0}^{ \sqrt{6} } \rho ~ \rho^2 sin \phi ~d \rho ~d \phi ~d \theta$
yep that looks correct, though you should include a proportionality constant for completeness. October 15th, 2017, 12:44 PM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 That would be correct if the density were equal to the distance from the origin. Instead it is "proportional" to that distance. The density is $\kappa \rho$ where $\kappa$ is the "constant of proportionality". Thanks from zollen Last edited by Country Boy; October 15th, 2017 at 12:46 PM. Tags challenge, spherical Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post proglote Physics 9 December 10th, 2018 06:20 AM Kinroh Calculus 3 March 29th, 2015 07:28 AM jhartc Differential Equations 0 December 6th, 2014 02:37 PM Shamieh Calculus 17 September 25th, 2013 05:39 PM TTB3 Real Analysis 2 February 16th, 2009 09:42 PM

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