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Let's say there's a creek.

Down in the creek, there is a current.

The vector field that describes this current is

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.)

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

To begin

But here's some trouble for me... I'm not certain on how to differentiate

Tell me, O somebody-who-is-doubtlessly-wiser-than-I, would

If that is so, I'll continue to find the dot product, and then begin the actual integration.

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**+ [0]**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**+ 1**k**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**+ 0**k**?If that is so, I'll continue to find the dot product, and then begin the actual integration.

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