WEBVTT
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welcome to this lesson in this lesson. Both of
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the definite integral. Using the integration by parts matter
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. So integration by part simply haven't two functions that
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can be expressed as u and DV. And that
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is he called to do the, uh, the
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evaluation of I am be the minus the integral from
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A to B over, do you? Okay,
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so the best part about this is to identify what
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is your you and what you see our debate.
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So here you is a function that is easily differentiable
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or when differentiated, it goes to zero quickly.
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Okay, so here will pick that. That's why
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. So that the you would be called to dy
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. Okay, Then again, we'll pick the deal
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. Very as okay. The hyperbolic sign of y
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y. So that here, if we took the
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integral e f y is because true they have a
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bolic costs of y. Okay, so none of
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that you have, uh, got that. We
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have the, um we have the way we can
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divide. Uh, we can find the we'll see
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why ass i you us? Why, then?
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May is close. Cool. Okay, so we
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value that at 02 Will come back to that later
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. Then I've been becomes then not do you becomes
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t y. Okay, so here. Yeah,
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Why then they hyperbolic costs. Now, if we
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integrate that, we have negative. A parabolic sign
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of why, Okay, Then you value it to
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the at this point. Yeah. Now the hyperbolic
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side why is is given us eat the power y
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minus e to the negative. Why all over to
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than the hyperbolic costs? Why is also giving us
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eat the power plus speed to the power negative y
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on to. So you will place those mhm then
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the whole of the differential. Uh, the whole
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of the integral. Yeah, now becomes, Why
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then needs the power. Yeah. Yeah, right
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. Yeah. So that is 02 Then we have
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this photos for the side. The hyperbolic sine.
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Yeah. Yeah. Okay, so now this gives
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us Yeah. If you put the zero out there
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because of this, it becomes zero. And that
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is gone. So would have only one by four
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black. The second part we have right this through
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. Okay. Mhm. And we have one minus
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one all over to, uh that is minus one
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. Okay, so that goes to zero. Well
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, yeah. I love this. This causes all
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that. So we have E Yeah, yeah,
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yeah. Okay. Oh, yeah, Yeah.
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Mhm. Okay. Yeah, yeah, yeah.
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Okay, so here. Wow, we have two
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e Thank you. Last to hope that. Oh
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, yeah. Not bad. Oh. Oh,
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Okay. So we're just multiplying to buy this so
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that we can let all of them sit on a
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bath. So this becomes very eat about you,
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then minus e to the power. Negative, too
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. All over. So this is that and of
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the lesson. And this is the answer for that
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definite integral. Yeah. Okay, thanks to a
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time, The end of the lesson.