(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

find the volume of the solid bounded by the graphs of the given equations:

r=1+cos∅

z=y

z=0

(the first octant)

2. Relevant equations

V=[itex]\int[/itex][itex]\int[/itex] rdrd∅

3. The attempt at a solution

So, I've been having trouble deciding what to integrate from and to. I converted the z equations into polar coordinates, so, z=rsin and z=0

[itex]\int[/itex][itex]^{2\pi}_{0}[/itex][itex]\int[/itex][itex]^{1+cos∅}_{0}[/itex] (rsin)rdrd∅

Mod note: revised LaTeX

[tex]\int_0^{2\pi} \int_0^{1 + cos(\theta)} rsin(\theta) r~dr~d\theta[/tex]

I found, from the first integration, [2∏]\int[/0][itex] r^(3)sin∅/3 d∅ and I need to plug in (1+cos∅) and 0 for r....but, this seems WAY too complicated having a trig function to the 3rd power.

I'm not even sure if I have the beginning correct. Can anyone help me out?

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# Homework Help: Find The Volume of A Solid

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