You can use the definition

Where C is a picewise smooth curve described by the parametric equation and F is a bidimensional vector field

By doing we can rewrite the line integral as:

Where we have a dot product. So for the problem you have and will depend, because you should take three line integrals over the three lines that closes the triangle, and each one will have a different parametrization.

So, let .

We can set the first line as the one who links to , links to , and links to . We followed a counter-clockwise direction.

Now we should parametrize , , .

For :

You can see that this line has

and

, so maybe the parametrization

with

should be nice for us.

For :

This line begins at the

then go to

, so we want that for some

, when t=a we will be at

and when t=b we will be at

. You can use the formula

. It follows that

with

.

For :

We can use the same formula again, so

give us

with

Now that we have the three parametric equations for each line we can evaluate:

for

Finally, we sum each value to get the final answer.

I apologize if I did any mistake, I don't have any book around here by now and I had to remember the whole process - that's why it lacks some deep explanations. I did my best and I hope it helps. Maybe the other guys around here can add some thoughts about it.