Im trying to verify this theorem for the following line integral
where is the triangle with vertices
I had no problem calculating the right hand side of green's theorem. However im struggling on the left hand side of the theorem.
Im thinking i need to get the line integral in terms of either x or y only ...?
I think i may have calculated the right hand side of green's theorem incorrectly.
i let and
this gave me and
so filling these into the equation i got
However im not sure if these limits are correct, aren't the inside limits of a double integral normally or ?
If you could answer this, it would be great