Line Integrals and Green's Thereom

Evaluate the following line integrals using the appopriate method. State any fundamental theorems that you use in your answers. (a) f F - dr where F(w,y) = ((3"n + :92, e'y + 1:2) and 0 consists of the arc of the curve C y = 0033: from (3220) to (35,0) followed by the line segment from (92730) to (~,0). (h) f F . dr where F(a:, y) = (yew-9 + 4cos(4a: + y), 329\"\" + cos(4.r + 31)) and C' is the curve 0 starting at (0, 0), going to the point (2, 0) along the m-axis, and then going around the circle :32 + 3,12 = 4 to the point (x/Z ). Part (a) Part (b) 2.0-, t u -':'J/////// .E ,,,,, z,'/l///// _ ...... III/I'll," ------- 11/////// 1.5- . \\\\\\\\\\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\\\\\\\\\ '\\ \\ \\ \\ \\ \\ \\ \\ \\ \\