(a) State Green's theorem in the plane, (b) Let I be the rectangle defined by 0 < x < 1 and 0

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A State Green S Theorem In The Plane B Let I Be The Rectangle Defined By 0 X 1 And 0 Y And The Curve C Be Its 1 (20.49 KiB) Viewed 263 times

(a) State Green's theorem in the plane, (b) Let I be the rectangle defined by 0 < x < 1 and 0 <y, and the curve C be its boundary, traversed anticlockwise. Consider the vector function F(x,y) = (3x’ay + 3x cos (ay))i + (x(1 - a*) – xa sin (ay)); Determine the value of a for which F. dr = 0. (c) Let y P(ty) Qla,y) 2? + y? 2² + y² and define the curve to be the circle of radius 1 centred on the point x = 2, y=0. Using Green's theorem show that -2x 1 + 2 cost dt = 0. 5 + 4 cost