- #1

filter54321

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## Homework Statement

I have a vector valued function that I need to integrate over a curve C (which I know how to do). I need to create a vector valued function r(t) for any position on the curve C (see the picture). r(t) is a defined area in the XY-plane and I'm pretty sure it needs a piecewise function.

## Homework Equations

See picture

http://img13.imageshack.us/img13/4368/graphgr.jpg

## The Attempt at a Solution

This might work, but I'm afraid of the undefined derivative.

r(t)=

0[tex]\leq[/tex]t<1 9t

**i**+0

**j**

1[tex]\leq[/tex]t<2 9

**i**+3(t-1)

**j**

2[tex]\leq[/tex]t[tex]\leq[/tex]3 (9-9(t-2))

**i**+(3-[tex]\sqrt{9(t-2)}[/tex]

**j**

r'(t)=

0[tex]\leq[/tex]t<1 9

**i**+0

**j**

1[tex]\leq[/tex]t<2 0

**i**+3

**j**

2[tex]\leq[/tex]t[tex]\leq[/tex]3 -9

**i**-3/(2[tex]\sqrt{t-2}[/tex])

**j**

You'll notice that the last part of the r'(t) vector is undefined at t=2. Is this appropriate? How do you do it?

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