Line Integrals

  • Thread starter popo902
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  • #1
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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 Im doing wrong??

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
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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).
 
  • #3
60
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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?
 
  • #4
Dick
Science Advisor
Homework Helper
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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.
 
Last edited:

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