Consider the vector field \mathbf{F}=\left(y+4-e^{-z}\right) \mathbf{i}+x \mathbf{j}+x e^{-z} \mathbf{k} (a) Evaluate the line integral of F along the path x=t-1, \quad y=0, \quad z=0, \quad 0 \leq t<2 (b) Evaluate

the line integral of F along the path x=-\cos t, \quad y=-\sin t, \quad z=0, \quad 0 \leq t<\pi c) Determine the curl of the vector field, i.e. V x F. Is the vector field F conservative? Briefly justify your answer. :) State what your answer to part (d) implies for your answers toparts (a) and (b).