The existing solution in Course Hero is unclear, especially with b (the parametrised part) and c (how -y dx is use). Please do not repost.

4. (Chapter 17,Section 19.1) 2 Consider the region R bounded by the lines 1' : 3:.-: and y : 3:1: and the parabola y : 4 :1: . (a) Find a 2-(1imensional vector eld E : (114(33, y), N(r, 3,0) such that n_%_l 5:1: ay_' (3) (b) Using this E and Green's theorem (Theorem 19.1.1). write the area integral / f 1 (M as R a line integral. [Hint Any function 1' : x) can be parametrised by :(t) : (t, f (1)) This can be used to parametrise both the line and the parabola]. (4) (c) Using this line integral, nd the area of R. (9)