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In the meantime, our AI Tutor recommends this similar expert step-by-step video covering the same topics. # Use a graph of the vector field $\mathbf{F}$ and the curve $C$ to guess whether the line integral of $$\mathbf{F}(x, y)=\frac{x}{\sqrt{x^{2}+y^{2}}} \mathbf{i}+\frac{y}{\sqrt{x^{2}+y^{2}}} \mathbf{j}$$ $$C \text { is the parabola } y=1+x^{2} \text { from }(-1,2) \text { to }(1,2)$$

## Line Integral is zero

Vector Calculus

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##### Top Calculus 3 Educators ##### Lily A.

Johns Hopkins University  ##### Kristen K.

University of Michigan - Ann Arbor ##### Samuel H.

University of Nottingham

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### Video Transcript

So this probably leaves a griffin party. You. But how? Computer the line to grow here. If so, Here first, first of is too Paramo tries. Disi is para Why was one Prospect Square? So if we said exit Ghostie wise one plus T square and X goes from negative one toe once O t simply goes from the fifth one too one. So what? This the integral articles from negative for are not quick. So this is our So we have our course. Aah! He won plastic a square. Now this air forfar off we replace all the exp i t Why buy one plus two square? So we got he over square. Rudolph X squared is T square on Why Squares tea forthe prostitute the score plus one. So here, forthe plus security Square plus one and similarly wise T square past one in the denominator. Is this him? And our priority would take that The repetitive component. Why? So you have a one in two tea, So a see the integral should be tea from that if one to one and the dot product of these two So t force plus street He square pross one He plus Teo Plus to teach So which is thiss And if we get it looks complicated But if I guess it correctly with this will be easy Use a problem assembly that this to be you that you will be forty que plus sixties forty que plus sixty which happens to be twice off Huma Reiter So here, but always the way you mean is even actually even easier than that. There's one thing I miss that Hopefully if I had no no So the function the int'l Grint is that our function? Which means it's sin naturally, if you change the teeth inactive t So that means if you integral with respect to interval that this symmetric with respect to zero Sure, I always get zero so you actually know don't need to do any conversation here. So as the funny part of this problem and I hope you figure out faster #### Topics

Vector Calculus

##### Top Calculus 3 Educators ##### Lily A.

Johns Hopkins University  ##### Kristen K.

University of Michigan - Ann Arbor ##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp