- #1
Ronaldo95163
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Hey guys I've been working some triple integration problems and I've stumbled across a question that I'm having problems with
So from the picture below my solution is incorrect and I can't seem to figure out where I went wrong. Is my setup for the integrals correct or is that where I've made my mistake.
1. Homework Statement
Q15 in the posted image
(Further Problems 15 pg 658 in the solutions posted)
So I found the intersection of the two surfaces z = sqrt(x^2+y^2) and z^2 = 4(x^2+y^2) and found this to be z=2a.
On the y-z plane the solid basically leaves a region bounded by z=2|y| and the sphere. Since z=2a then y = a. I used this to calculate phi as arctan(a/2a) and rho as 2asec(phi).
In the x-y plane is basically a circle of radius a...I used this to get my range for theta which was 0 to 2π
Then I setup the triple integral as follows(With 1 as the integrand because it's a Volume calculation for the solid formed)
My Right most integral for rho goes between 0 and 2asec(phi)
Middle goes from 0 to arctan(0.5)
Left most goes from 0 to 2 pi
My answer was 2a^3/π
So from the picture below my solution is incorrect and I can't seem to figure out where I went wrong. Is my setup for the integrals correct or is that where I've made my mistake.
1. Homework Statement
Q15 in the posted image
(Further Problems 15 pg 658 in the solutions posted)
Homework Equations
The Attempt at a Solution
So I found the intersection of the two surfaces z = sqrt(x^2+y^2) and z^2 = 4(x^2+y^2) and found this to be z=2a.
On the y-z plane the solid basically leaves a region bounded by z=2|y| and the sphere. Since z=2a then y = a. I used this to calculate phi as arctan(a/2a) and rho as 2asec(phi).
In the x-y plane is basically a circle of radius a...I used this to get my range for theta which was 0 to 2π
Then I setup the triple integral as follows(With 1 as the integrand because it's a Volume calculation for the solid formed)
My Right most integral for rho goes between 0 and 2asec(phi)
Middle goes from 0 to arctan(0.5)
Left most goes from 0 to 2 pi
My answer was 2a^3/π
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