How do I solve belows Greens Theorem problem using Calculus Made Easy on the TI89 ?

F·dr.C

F(x,y) =

y− cosy,xsiny

,

Cis the circle (x− 6)2 + (y+ 2)2 = 16 oriented clockwise

ANSWER:

Please do this: select F6 Vector Calculus , F2 8 : and enter as follows

[M,N]= [y-cos(y),x*sin(y)]

solve (*x* − 6)2 + (*y* + 2)2 = 16

(*y* + 2)2 = 16 – (*x* − 6)2

*y* = + – sqrt (16 – (*x* − 6)2) – 2

thus

y1,y2 =[ – sqrt

(16 – (x − 6)^{2} )

– 2 , sqrt (16 – (x − 6)^{2} )

– 2 ]

we have a circle centered at [6,2] of radius 4

thus x varies from 2 to 10

x1 , x2 = [2,10]

Voila!!!