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How can I determine $\int xy \;ds$ of a triangle with points $(0,0)$, $(1,0)$ and $(1,1)$ *The integral has the letter $C$, which I am not sure how to input here.

I know it may seem easy, but I am not sure of the working

I know that $ds = \sqrt{dx^2 + dy^2}$ but I do not even know what is $dx$ or $dy$ in this case.

Should I split into three segments? What is the simplest method to solve this?

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    Split into 3 segments. That said, the segments along the coordinate axes are zero, no?2012-12-23

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If you're talking about the line integral around the triangle, break it up into three parts corresponding to the three sides of the triangle. On the side from $(0,0)$ to $(1,0)$, $y=0$ so that integral is $0$. The integral from $(1,0)$ to $(1,1)$ has $ds = dy$ and $x=1$. The integral from $(1,1)$ to $(0,0)$, if you use $x$ as parameter, has $y=x$ and $ds = \sqrt{2} dx$.