WEBVTT
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All right, So we have the double inner girl
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spirit of three for flies of backs Rent X squared
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plus three. Why? T? Why t x
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OK, and so the way is written. It's
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written. Teo do the integral of prospective wife.
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First of treating X is a constant. We need
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to find an anti derivatives of this immigrant with respect
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to why, but Okay, first of all,
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this X is Constance Will pull that out on,
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then we're just left with brood X squared. Plus
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three. Why? Well, wake unjust if we
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wanted to let you equal X squared plus three.
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Why? And if we differentiate with respect to why
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we have do you his three? Why do I
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just one third to you? Okay. So we
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can replace this with you in a girl here.
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So if we evaluate our limits at y ankles for
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X squared plus that of twelve, then X squared
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. Plus teeming. And we have what's left Just
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square root of you, Teo. Okay. There's
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a change. Variable. All right, so this
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just becomes in a girl, Teo three of X
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and then this becomes well okay. You to the
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three halves. Three halves the infirm. X squared
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plus twelve X square plus fifteen. Okay, Thanks
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. It's, uh, simple, but that down
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we have X times X squared. Plus fifteen,
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two, three house, I guess. Okay.
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So, uh, there's one thing Africa here.
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So this is one third to you. So we
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have a factor of one third. And then way
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also have this factor. So there's a one third
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beacon factor out. We have this factor of three
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halves, so that makes this bacterial here two nights
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. Okay. All right. And then So let's
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finish this guy off. Sir, minus X squared
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plus twelve to the three house. OK. And
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so if we let know, we're going to have
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to really do too. Substitutions, But they're going
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to be the same S o. Let's let you
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be, uh, x squared fifteen and then civil
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noticed that to you is to the ex d X
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. It's one half to you, but knows that
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if we let you be x squared plus twelve,
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we're going to get exactly the same thing. So
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I guess technically, we should call this like you
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prime. Okay, so we want to evaluate this
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integral. So this is what we're calling you.
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This is where we're going. You prime. But
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do you really is the same things to you?
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Prime, You play There's an X here. Ex
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ddx So we made the substitution of RDX out here
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we have our x t x that'LL get absorbed with
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the factor one half. Okay, so this one
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half comes out the two nights becomes one night.
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Ah, in a girl now, any change our
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limits that the limits were going to be different for
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you and you primed. So for you, we
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have fifteen, two, twenty four. This is
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gonna be, uh, see new to the three
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house, and then plus, this is going to
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be you prime. And then we need to change
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our limits of integration to you, Primal. That's
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just going to be twelve to twenty one. You
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pry into the three house to you prime kid.
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And so we have I am both of these anti
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drivers. They're going to be the same. We're
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going to end up dividing by five halves, so
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that will make this a to over forty five.
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And we have you to the five halves gyrated from
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fifteen. Twenty four. Plus you prime to the
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five halves evaluated from twelve to twenty one, So
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this should just speak to over forty five times twenty
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four to the five halves dinos. Fifteen of the
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five halves plus twenty one to the five has minus
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talk to the focus.