F = 2xi - yzj + z^2 k ; The surface is the parabaloid z = x^2 + y^2 capped by the disk x^2 + y^2 <= 1 in the plane z = 1.
The answer in the book is 4pi / 3.
I believe we are supposed to use the divergence theorem to get the answer.
div F = 2 - z + 2z = 2 + z
SSS (2 + z) dV is the setup I get.
I think I have to convert to polar coordinates, but I'm not sure how.
What are my limits of integration here?
I want to say -1 <= x <= 1; -1 <= y <= 1, 0 <= z <= 1. Which would convert to polar as 0 <= theta <= 2pi; 0 <= r <= 1; 0 <= z <= 1.
How can I set this up in polar coordinates?
The answer in the book is 4pi / 3.
I believe we are supposed to use the divergence theorem to get the answer.
div F = 2 - z + 2z = 2 + z
SSS (2 + z) dV is the setup I get.
I think I have to convert to polar coordinates, but I'm not sure how.
What are my limits of integration here?
I want to say -1 <= x <= 1; -1 <= y <= 1, 0 <= z <= 1. Which would convert to polar as 0 <= theta <= 2pi; 0 <= r <= 1; 0 <= z <= 1.
How can I set this up in polar coordinates?