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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 9ti+0j
1[tex]\leq[/tex]t<2 9i+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 9i+0j
1[tex]\leq[/tex]t<2 0i+3j
2[tex]\leq[/tex]t[tex]\leq[/tex]3 -9i-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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