Question

Consider the vector field F(x,y,z)=xi+yj+zk.

a) Find a function f such that F=∇f and f(0,0,0)=0.
f(x,y,z)=

b) Use part a) to compute the work done by F on a particle moving along the curve C given by r(t)=(1+4sint)i+(1+sin2t)j+(1+sin3t)k,0≤t≤π2.