WEBVTT
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so in this video were asked to determine to grow
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were given that the s field is exciting. Hapless
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? Why do you have a boss? Excellent,
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K. And we're given that the position position Vector
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is co sign t. I have a Scientology at
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plus T K. Where t ranges from zero your
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pie. All right, So you want to find
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our private T? Basically, what we have to
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do is take the derivative of each turn. And
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Artie, So the derivative of co society is negative
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. Scientist, derivative of scientists, coastline and the
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derivative of tea is one. So this is our
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primary. All right? Now, how do we
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right after which is a function of X, y
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and Z in terms of teeth well organized. So
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we're gonna substitute to co sign t four x sign
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T for wine and t foresee. And this right
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here. So instead of X, we're gonna have
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close. I NT said a driver in f society
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and set of X y We're gonna have society time
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schools. All right, Great. So now,
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um, the line into grow Estela de or we
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can write it as integral film eight of beer that
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our prime have already determined. So r t goes
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from zero to pi. We determined that FBIs crow
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scientists I, Inti signed Tico Santi. So this
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right here and we determined that our prime is negative
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Sign t common co sign t cover one and then
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we have a DT. So if we are multiplies
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agree we compute the dot products Just throw safe from
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comes negative saying to you jizz negative scientist Coast 90
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Signed tea and coke times call scientists scientific oh society
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and scientific co sign tee times one is just so
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we can cancel one of these with you ever No
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, no to compute the integral of scientific on society
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. To you, what we can do is a
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little trick. So we're gonna we're gonna multiply,
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but we got out. We're gonna put it to
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here and you just get out of the blue.
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Put it to say we're gonna also put 1/2 so
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two times 1/2 his one. So we're just both
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of buying playing a sneaky one. And since when
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half of schools that we can put it to the
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upside Now, why did we do this? Because
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when we do this, we benefit we can We
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can change to scientific 0 70 using trade identities into
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signed to TVT. All right, so now how
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do we solve this? So this is an integral
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but we have signed to t on the inside.
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Well, does You might already know We're gonna use
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U substitution Czar. Gonna Yuriko to teach. Is
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that are you use just two tt So DT Megan
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, right? DT as you've divided back to.
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Okay, so now we're gonna rewrite are integral as
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1/2 injured Grove of 0 to 2 pi sign you
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d you divided by two a week of boldest 1/2
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to the outside. So now we have a 1/4
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on the outside. And then we changed The limits
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of the limit was originally from 0 to 5.
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But now we're gonna integrate with respect to you.
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So when we plug in zero for T, we're
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going to get you was equal to two times zero
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, which is zero. We plug in pi 40
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we're gonna use equal to two point and then now
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we have 1/4 in Jerusalem, zero to buy,
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sign you do you and the integral of sine of
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you did you is just negative coast like and then
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now are limits of our limits. Become to call
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a 0 to 2 pi. And we can take
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this negative one and we can pull it to the
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outside. So we have negative one for and now
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co sign U minus. Sarko signed two by minus
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minus two co sign of zero. Well, go
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sign up to fly is one co sign of zero
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is also one. So now we have one minus
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one, which is zero. So they're lining to
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grow is