# Do I have to use this formula to calculate the integral?

I have the following exericse: "Calculate the integral $$\oint_C{(x+y)}ds$$ where $C$ is the line segment $x=t, y=1-t, z=0$, from $(0,1,0)$ to $(1,0,0)$."  To calculate this integral do I have to use the following formula? $$\oint_C{f}ds=\int_a^b{f(x(t),y(t),z(t)) \sqrt{(x'(t))^2+(y'(t))^2+(z'(t))^2}}dt$$

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## 1 Answer

You have $ds = \sqrt{2}\, dt$. Do this and it's not hard.

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How did you find this equality? – Mary Star Mar 12 '14 at 0:02
You have $x'(t)=1,y'(t)=-1,z'(t)=0$ – Ross Millikan Mar 12 '14 at 0:06
So we get to that by using the formula of my first post, don't we? – Mary Star Mar 12 '14 at 0:20
You are there...... – Ross Millikan Mar 12 '14 at 22:34
Yes, that is right. – Ross Millikan Mar 12 '14 at 22:45