Let's say there's a creek. Down in the creek, there is a current. The vector field that describes this current is Cur[x y z] = [(ðy)^x]i + [(y^4)+(xyz)]j + (2z + e^z)k Nota bene: ð = pi The force is in Newtons. X, Y, and Z are the spatial dimensions in meters, whose origin is a piece of bait in this case. You see, there's also this guy who's fishin' in the creek. His bait's down there, situated on the origin. A fish sees it, and circles around it one complete time. The fish is unsure during this period, and maintains a distance of one meter. This motion takes exactly 2ð seconds for the fish. So, the motion can be described as a vector-valued function of t, time (sec.) Fis(t) = [cos(t)]i + [sin(t)]j + k How much work is done by the fish? Ok... so I made this problem up... that's why it's so weird. :) I need help setting it up. I know I need to use a line integral. The upper limit, t, in seconds, will be 2ð, while the lower will obviously be 0. So, first off, I need to find the integrand, which is the dot product of Cur[Fis(t)] and Fis'(t). To begin Cur[Fis(t)] = [(ð*sin(t))^cos(t)]i + [sin(t)^4]j + 1k But here's some trouble for me... I'm not certain on how to differentiate Fis(t). Tell me, O somebody-who-is-doubtlessly-wiser-than-I, would Fis'(t) = [-sin(t)]i + [cos(t)]j + 0k ? If that is so, I'll continue to find the dot product, and then begin the actual integration.