Question

Calculate the flux of the vector field F (x,y,z)=⟨6,z,yz⟩ through the surface S which is parametrized by r (u,v)=⟨4v², v cosu,2vsinu⟩ for 0≤u≤π/2 and 0≤v≤1

Answer 1

To calculate the flux of the vector field F through the surface S, we need to evaluate the surface integral ∫∫S F · dS.

Step-by-step explanation:

To calculate the flux of the vector field F through the surface S, we need to evaluate the surface integral ∫∫S F · dS. The surface S is parametrized by r(u,v) = <4v², v cosu, 2vsinu> with 0≤u≤π/2 and 0≤v≤1. To find the unit normal vector to the surface, we take the cross product of the partial derivatives with respect to u and v, giving us N = r_u × r_v. Then, we evaluate the dot product F · N and integrate over the domain of the surface.