do all the questions please

8. Write a Riemann sum for a flow integral of a velocity vector field. 9. a) A vector field in 3D is undefined for I = 1. Suppose its curl is zero. Can we conclude from this that the circulation over any closed curve in the domain is zero? b) For this vector field, suppose we found a potential function that is defined everywhere. Can we now conclude that the circulation over any closed curve in the domain is zero? c) Can a potential function be found if the curl is not zero? Justify your answers using definitions and theorems. 8. Write a Riemann sum for a flow integral of a velocity vector field. 9. a) A vector field in 3D is undefined for I = 1. Suppose its curl is zero. Can we conclude from this that the circulation over any closed curve in the domain is zero? b) For this vector field, suppose we found a potential function that is defined everywhere. Can we now conclude that the circulation over any closed curve in the domain is zero? c) Can a potential function be found if the curl is not zero? Justify your answers using definitions and theorems