1. ## line integral helps

Hello,
I would very much appreciate help with this .I just dont get it .(and Im not supposed to use greens theorem)thanks.just the normal line integral.
(2x − y + 4)dx + (5y + 3x − 6)dy around a triangle in the xy-plane
with vertices at (0, 0), (3, 0), (3, 2), traversed in the anti-clockwise direction..

2. ## Re: line integral helps

Can you parameterise each of the segments that make up the triangle?

3. ## Re: line integral helps

Originally Posted by Prove It
Can you parameterise each of the segments that make up the triangle?
Hello!

AB has coordinates (0,0) and (3,0)-->parametrization is x=3t

BC has coordinates (3,0) and (3,2)-->parametrization x=3+3t,y=2t
CO has coordinates (3,2) and (0,0)-->parametrization ,x=3;y=2

4. ## Re: line integral helps

Originally Posted by n22
Hello!

AB has coordinates (0,0) and (3,0)-->parametrization is x=3t What about the y parameterisation?

BC has coordinates (3,0) and (3,2)-->parametrization x=3+3t,y=2t x is constant, why have you parameterised it to change?
CO has coordinates (3,2) and (0,0)-->parametrization ,x=3;y=2 Why do you have x and y as constants when they clearly change?
The only one I agree with is your x parameterisation for AB and your y parameterisation for BC. I also assume that the third segment should be CA, not CO.

Also, use a different parameter for each segment.

5. ## Re: line integral helps

Originally Posted by Prove It
The only one I agree with is your x parameterisation for AB and your y parameterisation for BC. I also assume that the third segment should be CA, not CO.

Also, use a different parameter for each segment.

Going anticlockwise:
for path 1:x=3t,y=o,z=0(do i need to mention this ?)
for path2: x=3,y=2t
for path 3:3-3t;y=2-2t