Calculating Line Integral of C from (1,0) to (3,1)

[popo902]

Homework Statement

Suppose C is the line segment from the point (1,0) to the point (3,1). Compute the line integral
intC {( xdx + (x + y)}dy

Homework Equations

The Attempt at a Solution

i graphed the line that connects(1,0) to (1,3) and i got the equation of that line
so y = 1/2(x-1) or y=1/2x -1/2
dy= 1/2
i set x=t
and dx=1
my endpoints of integration became t=1 and t=3
then i plugged everything in
so my integral looked like this
1<= t<= 3 {(t(1) + (t + (1/2t - 1/2)) }1/2

i simplified that to this:
5/4t - 1/4

and i integrated that over 1->3
and i got 9/2...but it's wrong?
can someone tell me what I am doing wrong??

 

[Dick]

I could fuss about your notation a bit but I won't. In {(t(1) + (t + (1/2t - 1/2)) }1/2 you've got the (1/2) from dy multiplying the dx part too. Make it t+(t+(t/2-1/2))*(1/2).

 

[popo902]

oh i don't multiply the dy by the whole thing?
so i seprate the dx from the dy
but the points of integration at t are still the same tho right?

 

[Dick]

I think you want to integrate x*dx+(x+y)*dy. A line integral (x*dx+(x+y))*dy doesn't make much sense. Everything else seems ok.