Lomion
Dec12-04, 09:15 PM
Hello!
This is a question from one of our past exams, and it's had me stumped for the past hour. The question states:
The cylinder x^2+y^2=2x cuts out a portion of a surface S from the upper nappe of the cone x^2+y^2=z^2.
Compute the surface integral: \int\int (x^4-y^4+y^2z^2-z^2x^2+1) dS
I'm mainly having trouble getting started. What exactly is the surface that we're supposed to evaluate the integral over?
My guess on this question is that I should parametrize the cone:
T(u,v) = (vcosu, vsinu, v)
And use that to find T_u X T_v.
But what do I do after this? In order to find the limits of integration for u and v, do I use the conditions given by the cylinder? v = 2cosu?
Using that still doesn't give me the numerica limits for v, though.
Help, anyone?
This is a question from one of our past exams, and it's had me stumped for the past hour. The question states:
The cylinder x^2+y^2=2x cuts out a portion of a surface S from the upper nappe of the cone x^2+y^2=z^2.
Compute the surface integral: \int\int (x^4-y^4+y^2z^2-z^2x^2+1) dS
I'm mainly having trouble getting started. What exactly is the surface that we're supposed to evaluate the integral over?
My guess on this question is that I should parametrize the cone:
T(u,v) = (vcosu, vsinu, v)
And use that to find T_u X T_v.
But what do I do after this? In order to find the limits of integration for u and v, do I use the conditions given by the cylinder? v = 2cosu?
Using that still doesn't give me the numerica limits for v, though.
Help, anyone?