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.
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.