1. ## Line Integral

Evaluate the integral: (x + y)dx + ( y - x)dy as a line integral

where
G is the path, from (1,1) to (4,2), described by a straight line: 3y - x = 2

I tried using green's theorem but I don't think this is correct, could someone help me with which method to use, thanks

2. Originally Posted by jpquinn91
Evaluate the integral: (x + y)dx + ( y - x)dy as a line integral

where
G is the path, from (1,1) to (4,2), described by a straight line: 3y - x = 2

I tried using green's theorem but I don't think this is correct, could someone help me with which method to use, thanks
Sure. If $x = 3y - 2$ then $dx = 3 dy$ so

$
\int_c (x+y)dx+(y-x)dy = \int_1^2 (3y-2+y)3dy +(y-3y+2)dy
$

Now simplify and integrate.