Line Integrals of piecewise curves to find mass of wire

  • #1

Homework Statement


A wire lies along the piecewise linear curve extending from the point (4,3) to the point (6,15) to the point (12,15). If the density of the wire is given by (xy)=3xy+2y, use a line integral to find the mass of the wire.

Homework Equations





The Attempt at a Solution


So I have to find two C (C1 and C2) where C1=(4,3) to (6,15) and C2=(6,15) to (12,15) and do two integrals and add the two up. I Assume I have to parametrize using (1-t)R0+tR1 for each C1 and C2.
But then I have to substitute for t in all the x and ys and that gets really ugly especially the ds part which is sqrt((3y+2y)^2+(3x+2)^2) and I have to substitute my t components and then I have to do it for C2. This problem seems way too difficult and easy to make errors. Is there an easier way?
 

Answers and Replies

  • #2
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I assume you're integrating 3xy+2y along those two paths. For the first path, a parameterization is y(t)=6t-21 and x(t)=t so that would be:

[tex]\int_4^6 \big(3t(6t-21)+2(6t-21)\big)\sqrt{1+36}dt[/tex]

and the second one would be equally easy to set up and evaluate
 
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