Question

Let S be the surface reproduced below and parameterized by

u, u) = (2-u

b) Calculate Vector Field Flow

through S, if the surface is oriented at point (2, 0, 0) by the normal vector  ⃗n =  ⃗k.

Answer 1

"Given Let 'S' be the surface reproduced below and Parameterized by R^rightarrow (u, v) = (2 - u) cos (v)i^rightarrow + (2 - 4) sin(v) j^rightarrow + u^2 k^rightarrow Given: F(x, y) = y^2 i - 2^2 j + y^2 k R(u, v) = (2 - u) cos vi + (2 - u) sin vj + u^2 k R_u = -cos vi - sin vj + 2uk R_v = -(2 - u) sin vi + (2 - u) cos vj + ok R_u times R_v =