Find the surface area of the part of the cone z = sqrt[(x^2 + y^2)] lying inside the cylinder x^2 - 2x + y^2 = 0.
2. The attempt at a solution
Partial Derivative x = x/sqrt(x^2 + y^2)
Partial Derivative y = y/sqrt(x^2 + y^2)
sqrt((Partial Derivative Y) ^2 + (Partial Derivative at Y) ^ 2 + 1) =
sqrt[(x^2 + y^2)/(x^2 + y^2) + 1] = sqrt
the surface area =
integral on E of sqrt r dr d(theta),
where E is the region (r, theta)|(0 < r < 2, 0 < theta < pi)
My books solution has the body of the integral as 5, and E as (0<r<1, 0<theta<pi)
I'm pretty sure I've just made an algebraical mistake in the body, but for the limits I'm confused. I don't know how to treat a cylinder that isn't centered at the origin. I thought r was always the distance from the origin... is it really the distance from the center of the cylinder?
Thanks for any help or advice you can give me.