Line Integral Question (Vertical line issues)

  • Thread starter Lothar
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  • #1
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Homework Statement


A wire lies along the piecewise linear curve extending from the point (2,2) to the point (12,4) to the point (12,9). If the density of the wire is given by (xy)=2xy+6x, use a line integral to find the mass of the wire.


Homework Equations





The Attempt at a Solution


I know I need to do two separate line integrals and add them.

For the first half (2,2 to 12,4) I got
integral from 2 to 12 of [(2(t)((1/5)t+(8/5))+6t] sqrt(1+(1/5)^2) which comes out to be 890.629

For the second part, I know it should be integral from 4 to 9, but I'm having issues finding the correct equation for the line from (12,4) to (12,9).

I've tried just using the y parametrization of p(x,y) which is <t,(1/5)t+8/5>, but I'm not getting the right answers.

Can anyone help me out with this? I have an exam during the next week.

Thank you.
 

Answers and Replies

  • #2
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A parametric equation of the line segment with the starting point (12,4) and end point (12, 9) is: r(t)=(1-t)(12,4)+t(12,9)=(12, 4+5t), where 0=<t=<1.

That is x(t)=12, and y(t)=4+5t. Now just parametrize the linear density, and integrate. Don't forget the ds term though.
 

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