# Line integral over a triangle

## Homework Statement

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.

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## Homework Statement

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.
Both parameterizations would work, but you haven't provided enough detail for us to see where you went wrong. In either case, x is a constant, so the dx term drops out.