# (vector calculus question using stokes theorem and line integrals with respect toarc

#### earn1087

1. The problem statement, all variables and given/known data

let c be the curve of intersection of the cone z= sqrt(x^2+y^2) and the plane 3z= y+4, taken once anticlockwise when viewed from above.

(i) evaluate
∫c (sinx - y)dx +(x+cosx)dy + (e^z + z)dz

(ii) let s be the surface of the cone z= sqrt(x^2+y^2) below the plane 3z= y+4 and above the xy plane.

let F = (sinx - y)i +(x+cosx)j + (e^z + z)k

evaluate
∫∫s [(curlF) . nds], where n points downwards .
2. Relevant equations

3. The attempt at a solution
for(i) i attempted to create parameters however it creates a messy equation to integrate. i also don't know if i used the parameters correctly.

this is not homework, its the final question of a revision paper with no solutions

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