How do I solve belows Greens Theorem problem using Calculus Made Easy on the TI89 ?
F · dr. C F(x, y) =
y − cos y, x sin y
, C is 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!!!