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Line integral problem, lost when they sub, have work written out!

  1. Mar 28, 2007 #1
    Hello everyone~

    I have the following problem, its done in the book but i'm lost on how they came to the final answer.

    Evaluate the line integral:

    Integral over C xy dx + (x-y) dy, C is the line segment from (0,0) to (2,0) and (2,0) to (3,2).

    C = C1 + C2;
    On C1: x = x, y = 0;
    dy = 0 dx,
    0 <= x <= 2;

    On C2: x = x; y = 2x-4;
    dy/dx = 2; => dy = 2 dx;
    2 <= x <= 3;

    This all makes sense to me, but then they have:

    Integral over C xy dx + (x-y) dy = integral over c1 xy dx + (x-y)dy + integral over c2 xy + dx + (x-y) dy;

    = integral from 0 to 1 (0 + 0) dx + integral 2 to 3 [(2x^2 -4x) + (-x + 4)(2)] dx;


    I see where the 2 came from in the 2nd part, because dy = 2 dx; but why is it (0 + 0) in the first part, and also where did they get 2x^2-4x? or the -x + 4?

    Thanks!
     
  2. jcsd
  3. Mar 29, 2007 #2
    All you answers can be found here
    First integral: What does y and dy =?
    Second integral: What is y=?

    It may appear irrelevant here, but the limits of the first integral should be 0 and 2.
     
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