WEBVTT
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So in this video, we're s too. Show
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that the line integral along the curve off our deal
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are are dot your is equal to 1/2 the magnitude
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of bar B square minus the magnitude of our age
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square as t goes from a to B. Alright
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, So first of all, our our t r
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curve or position Victor So we can write that in
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terms of x, y and Z So it's except
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e I have much wife t dream had Muzi of
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t. K. All right now, we can
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, uh, write this as a vector. So
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bars just exit t call alive t columnist in your
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teeth and then are are fine. We just take
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the derivative bets. So our prime of tea is
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just experience. Do you call the white crime of
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commas? All right, Now take the right hand
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side of the integral along. See our our dog
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to your we can write that as integral in terms
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of teas, though it's the integral from eight of
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the off our t dot R. All right,
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so we know what our He is just excellently life
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museum. And we know what our primal is just
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our privacy. Sorry. Experiment. You like travel
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to use. Okay, so when that wouldn't be
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multiply this out. We get integral from a to
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B. Yes, except E except in Times Express
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, if you aspire to times like private was zero
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times the property. All right, so now we
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need to notice We know that what is accepting expert
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, will we take the derivative of X square of
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TV? Well, if we use our changeable so
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we know that this is a function of the functions
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we're gonna user change room So it's gonna be d
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of x square t by the X, and then
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we're gonna multiply that by D of x of t
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you right, Because we know that excellent option t
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So this is gonna be the change will. So
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this is our chamber. But what's the derivative of
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X squared with respect, X levels just to apps
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. And once the exp i t t Well,
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that's just express So and here we notice we have
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except e x times expert, but are only issues
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that we have. This little happen front so exits
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off. We divide both sides by two. We're
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going to get x x times X prize is 1/2
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that derivative. Well, thanks square. And then
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we can do the same thing for a while and
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see, So we're going to get this right over
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here. So they substitute xx bribe. I would
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have the derivative Rex square with respected T. And
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if we substitute why times like prime with 1/2 the
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derivative before squared, respected Tiu. And if we
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substitute ze time, see a prime by 1/2 the
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derivative of deceased square. Then what we can do
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is we notice that there's a common factor off what
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happened. So we pull this one after the upset
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. Remember, If we're gonna take the integral off
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a derivative by the fundamental theoretical calculus they can't select
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. So what? We're left with its X squared
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of going from A to B. Why squared of
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t going for be a to be and the square
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of people. Now if we pluck me, is
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it We're gonna get 1/2 x squared of be Linus
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X squared away Plus why scared of B minus y
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spirit of a plus the square to be by the
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sea script. I'm just rearranging putting the negatives together
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and depositors together. We're going to get this fine
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. It's this. I don't know. What do
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we notice? We notice an expert of people swear
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spirit of people's the spread of B. Well,
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that's just the magnitude of B squared. We also
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noticed I get X were debate plus y squared of
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any Percy spread of able. That's just the magnitude
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of Barbie Square. We have 1/2 Barbie outside and
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that we showed. I want you to be sure
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1/2 times thing magnitude of R B squared, minus
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the magnitude of our school. That's the link.