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Evaluate $\int _ { C } \frac { 1 } { x ^ { 2 } + y ^ { 2 } + 1 } d s$ where $C$ is given in the accompanying figure.

$\int_{C} \frac{d s}{x^{2}+y^{2}+1}=\pi$

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we have three paths. So see one C one is tea by what's his friend's ears Warm C two is one times I pull a Steven strain for again single Main in C three will be one with CNN's I Waas Wyndham's J against the same domain. C four is woman a sequence J So the buy components is zero again A symbol mean. Okay, So for C one, the model figurative will be one. C two is also one C three is also one deathless C four again. So so one. Everything's very neat. Oh, the not helping a charity function. It's one. Okay, that's calculates this lot into girl. Here we have C one over X squared, plus what's worthless. Wendy s is actually. See, I signal I was 212 for 10 X squared X I squared. Plus why? I swear. Plus one. Yes. So we're plugging the value voyage each path, respectively. And that look, we're gonna have finally have this integral. So 0 to 1. The three over T sward loss. One watches are constancy. Was 0 to 1. The tea over to swarm us to something regarding the Arkham Santy and the 0 to 1. Did she? One minus t squared. Plus two. This is, um, against those arcs. Dungeons. What? Ah, for some politicians and for C four city over one month's to swear close one. So you got it all being too girl. The final answer is R equals two. How you were two plus swore to tons are tensions square to over two That's it.

University of Illinois at Urbana-Champaign