Let F? =(5z+5x4)i? +(6y+7z+7sin(y4))j? +(5x+7y+6ez4)k? . (a) Find curl F? . curl

Question

Let F? =(5z+5x4)i? +(6y+7z+7sin(y4))j? +(5x+7y+6ez4)k? .

(a) Find curl F? .
curl F? = 0

(b) What does your answer to part (a) tell you about ?CF? ?dr?  where C is the circle (x?10)2+(y?15)2=1 in the xy-plane, oriented clockwise?
?CF? ?dr? = 0

(c) If C is any closed curve, what can you say about ?CF? ?dr? ?
?CF? ?dr? = 0

(d) Now let C be the half circle (x?10)2+(y?15)2=1 in the xy-plane with y>15, traversed from (11,15)to (9,15). Find ?CF? ?dr?  by using your result from (c) and considering C plus the line segment connecting the endpoints of C.
?CF? ?dr? =

need help with C

Explanation / Answer

c)
Because the field is conservative, i,e curl F = 0,
we can state that integral F.dr will be PATH INDEPENDENT, it wont depend on the path, no matter what the path is, the value will always be the same

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