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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!

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# Homework Help: Line integral problem, lost when they sub, have work written out!

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