WEBVTT
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So in this question, we're asked to use a
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program or calculator in order to determine the line integral
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. But before that, we have to set up
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our into grow that rocketed to a calculator or a
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program t determine the value of the range. So
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we're given that, uh I mean, it's just
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x y I have assigned jihad, and we're also
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told that the position vector is e t. I
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had Plus is the power of negative t swear jihad
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where t varies from 1 to 2 now, first
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of all, we want to write everything in terms
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of so for x. So in f of x
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and Y or expert and a plug in you did
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the ballot 54. Why? We're gonna plug in
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either the power. Okay, So extension allies just
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either the tee times eat of the power of Negative
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t Square, and then you we just at the
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experience. So what we're gonna get is be to
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this under Skinner, so we quickly do it.
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You just get me to the power T minus square
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, then sign of why. So instead of wired
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a plug in even even negative square to become signed
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all right. And then our pride we just take
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the derivative of are so you know, the tea
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becomes remains Even the tea we need to the negative
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square becomes negative. Two teeth e to the negative
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T square. So we should we should know how
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to do these into girls These derivatives from are so
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now we determine this too. And then now we
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proceed to determine are lining to grow. So another
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way to write the line integral is like this where
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everything is in terms of tea and so the integral
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from wanted to So we're going to take the dot
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product of asked at our price. So that's basically
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done by multiplying the first term here by the first
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term here, second term. So what we get
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gazing row foam Wanted to eat to the T minus
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T square turns you to the T plus sign into
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the negative t square times negative to TV to the
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negative to square. Thank you. So we're gonna
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So what we can't is the falling. So we
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just add c two TV dynasty squares. We'll get
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to t ways to swear And, uh, there
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is no other simplification. We can do so again
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. The problem tells us that we can use software
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, so we use software we get. The final
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answer is 1.96334 The whole idea is to get to
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this point, and then we're not gonna race their
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time determining this integral, because the question says,
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just poured it into a calculator or some algebra software
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get divine.