Let ?⃗ =(5z+5x^3)i+(6?+7?+7sin(?^3))j+(5?+7?+6?^(?3))k
(a) Find curl ?⃗
curl ?⃗ =
(b) What does your answer to part (a) tell you
about ∫??⃗ ⋅??⃗ where C is the circle (?−25)^2+(?−30)^2=1 in the
xy-plane, oriented clockwise?
∫??⃗ ⋅??⃗ =∫CF→⋅dr→=
(c) If C is any closed curve, what can you say
about ∫C ?⃗ ⋅??⃗ ?
∫C ?⃗ ⋅??⃗ =
d. Now let ? be the half circle (?−25)^2+(?−30)^2=1 in the ??-plane with ?>30, traversed from (26,30) to (24,30). Find ∫C ?⃗ ⋅??⃗ by using your result from (c) and considering ? plus the line segment connecting the endpoints of ?.
Let ?⃗ =(5z+5x^3)i+(6?+7?+7sin(?^3))j+(5?+7?+6?^(?3))k (a) Find curl ?⃗ curl ?⃗ = (b) What does your answer to...
(1 point) Let +4z + 4 sin (a) Find curl F. curl F- (b) What does your answer to part (a) tell you about JcF dr where C is the circle (x 30)2 + (y - 10)2 1 in the xy-plane, oriented clockwise? (e) If C is any closed curve, what can you say about fcFdr? (d) Now let C be the half circle (-30)2-cy-10)2-1 in the xy-plane with y 10, traversed from (31, 10) to (29, 10). Find F...
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