💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here! # Use a graph of the vector field $\textbf{F}$ and the curve $C$ to guess whether the line integral of $\textbf{F}$ over $C$ is positive, negative, or zero. Then evaluate the line integral.$\textbf{F}(x, y) = (x - y) \, \textbf{i} + xy \, \textbf{j}$,$C$ is the arc of the circle $x^2 + y^2 = 4$ traversed counter-clockwise from $(2, 0)$ to $(0, -2)$

## $3 \pi+\frac{2}{3}$

Vector Calculus

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##### Top Calculus 3 Educators  ##### Heather Z.

Oregon State University ##### Samuel H.

University of Nottingham Lectures

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### Video Transcript

Oh, for the next few problems. How computers the problem. But I our lives a graphic calculator, part of you and for the estimation of positive at heaven's hero, you can look as the explanation on problems seventeen eighteen off this section. So we want to paramo tries this curve. It is a circle from two zero, which is the right hand side of sorrow two zero negative too, which is a South pole circle. So we use a standard permit realization Ex seals to co sign T. These are scores four stars to my host to scientist and we called Who is this? Like a ghost from the right hand side to the apartment. So So she's from Oh, well, well, so I was a tea from zero two negative pie over, too. All the indicators stuff started to the larger number two a small amber rather than just writing a range of t, which might be a little bit confusing. Uh, so, using this setup, we know this is our off. He's over his half off. Our tea should be X minus y to co sign T minus two side. He and X Why should be four scientists Ho Sai Inti, these are prime team Negative two side he to co sign t Just take the derivative component wise. So what is integral? It's a girl Goes from zero two negative pie over too. So the product of these Sorry, the product's force I squared t minus four Scientific society plus eight scientific cause I security on us. As for us raise science Chris one minus cause I two tea over to so there should be two minus to co sign Tootie miners for scientific co society plus his sign Cose i scurti TT So you're a writer and tight, a repetitive A to t minus Signed Tootie So you take the roof here becomes to call sign Tootie And this one this way is simply look at it as they use up. Probably use you for society than the other power be Do you so being with you So you should be Teo sine squared t and similarly this one You look at the use a problem or you host call society as he and you should get co sign to the people that the rift is nephew scientist We should put an active here. Come on we have hate and divide by three. So you take the rib Him? Yes, three coz I score tears three, cancel the denominator Times and net website Here's our inside the room with you So you probably nephew pirate too weak connective pie minus sign pi So sign negative pie which is a simple sign Pi and, uh that should be zero sai square Negative pirate too. So this one is signed part nephew power to his next if one so scores one. So you are minus two miners coz I never power to zero so the last time should be zero minus If we promise your first served seven times hurt from ho zero the last time she gives us cause and heroes wants on minus eight over three Always should get minus pi minus two plus hit over three So this is six over three part eight hours Remind six officers are to over three minus pi #### Topics

Vector Calculus

##### Top Calculus 3 Educators  ##### Heather Z.

Oregon State University ##### Samuel H.

University of Nottingham Lectures

Join Bootcamp