I'm attempting Q 3 from ch 16.4 of Stewart (p 1060).
We are required to find the line integral where C is the triangle with vertices (0,0), (1,0) and (1,2).
The line integral is
Int xy dx + x^2*y^3 dy
The Attempt at a Solution
I'm having trouble parametizing the vertical line between (1,0) and (1,2).
I'd let y = 2t and x = 1, but got the wrong final answer. I suspect it's because line (1,0) to (1,2) was incorrectly expressed.
I then wanted to integrate in terms of dy, with terminals for y of 0 and 2, and parametizing y in terms of y, but where does that leave the dx in the first part of the equation?
I imagine it would be easier to use Green's Theorem, but the question specifically requires the use of line integrals.