I'm struggling with what to do for this problem. My phi bounds are pi/3 to pi/2. My theta bounds are 0 to 2pi. My rho bounds are 0 to 2. My integrand is rho^2 times sin(phi). Can you please give me a clue as to where I'm going wrong? I took this problem to the tutoring center and they couldn't figure it out either.
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Let's see: z=3r means ρ*cos(φ)= 3ρ*sin(φ) so φ = tan^{-1}(1/3) =0.322 radians or 18.43 degrees. Your only mistake was jumping to the conclusion that webwork would default to a clean and easy lower bound.
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