WEBVTT
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were given a solid S. And we have to
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find the volume of this solid. The stars.
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We're told that the base of the solid is the
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same base has an exercise 58 but the cross sections
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perpendicular to the X axis are isosceles triangles with a
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height equal to the base. So from exercise 58
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the base was actually a parabola. It's the parabola
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mm uh Y equals one minus X squared and the
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line Y equals zero in text you a lot.
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Okay? He said fucking jews control right? Imagine
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this is saying it as okay. Yes. So
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first you want to find the area of one of
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these triangles, right to do this, we need
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to find what the bases and to find the base
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truck called B. This is just the value of
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why? Which is one minus X. Squared.
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So the top curve minus the bottom curve we'll keep
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. Mhm. Now their base. Well, we're
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told the area of the assassins triangle. This is
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one half times the base times the height. And
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we're told that the height is equal to. Don't
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fuck with me bro. I was. And base
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this is the same as one half B squared which
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is one half times one minus x squared squares,
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racist. So this is the area of one of
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the triangles. In terms of X. Using the
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cross section interpretation, our volume is the integral From
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what we see on our base. The X range
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is from negative 12 positive one of our area A
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. Of X. Dx. This is one half
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times the integral from negative one positive one of one
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minus X squared squared ultimate dx. Yeah. Now
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if you foil this out and take anti derivatives,
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this is a pretty easy integral to evaluate. And
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you should get 8/15. Did you could get sucked
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wrong. Mhm.