Answer:
The integral [tex]\int F \bullets ds [/tex] is 0.
Step-by-step explanation:
A parameterization of curve C can be:
X (t) = cost 0 <= t <= pi
Y (t) = sint 0 <= t <= pi
r (t) = costi + sintj
r '(t) = -sinti + costj
[tex]Fds = [-costsin^3t + sintcos^3t] dt[/tex]
The integral [tex]\int F \bullets ds [/tex] is given by:
[tex]\int _0^{\pi }\left[-costsin^3t + sintcos^3t dt\right]dt[/tex]
[tex]= \int _0^{\pi }-sin ^3tcostdt + \int _0^{\pi }sintcos^3tdt = 0[/tex]
