Cordde the Integral 'sany drove'cosy dy. (a) Show that the integral is independent of the path of integration chosen by using the Fundamental Theorem of Line Integrals (Theorem 16.5.1). Hint: Conide the wetor field E - (e'sing, e'easy) and prove that it has a potential function.] (4) (b) Compute the integral i by transforming the integral to an ordinary single integral (see Saction 15.3) i. using the Fundamental Theonan of Line Integrals. [11] 2 ( Section 14.6, Chapter 17) Let I be a region in R' bounded above by the plane 2 - 1 and below by the paraboloid 2-847. Let S be the suface of V (consisting of the flat dise on top and the surface of the paraboloid below it). (a) Compute the volume of V' reing cylindrical coordinates. (10) (b) Sketch 5 and the XY-projection of 5. (e) Use a surface integral to cuduate the area of 5. [21] 3 (Chapter 10) Let E be a comerutive vector field in R'. (a) What is the definition of a conservative wetor fickl? 12[b) Prove that if C as any chard path in RY, then End-0