WEBVTT
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were given a solid S and rest to find the
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volume of this solid, we're told the base of
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S. Is the region enclosed by the parabola.
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Y equals one minus X squared and the X.
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Axis and the cross section is perpendicular to the y
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axis are squares. That's something good. What does
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he said have a good woman that I've never seen
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? Well to find the volume will find the area
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of each of these squares. To find the area
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of the square. As you want to find the
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length of one of these sides of the squares,
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which is the distance from one side of the parabola
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to the other. To do this, we want
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to solve for X as a function of Y.
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So we have rearranging X equals mm plus or minus
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the square root of one minus Y. And therefore
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it follows their side length. S is going to
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be two times the square root of 1-.
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Why. Yeah. And therefore our area of the
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square as a function of why? Well this is
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S squared Which is four times 1-Y. Really
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. And now using the volume interpretation uh Benadryl,
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the volume is the integral from why ranges. Yeah
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. More of the purest I think. Yeah,
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I've never seen it sort of the from zero the
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x axis up to the Vertex of the Parabola one
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of the area A. Of Y. Dy.
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Would you think? Mhm Towards you harry If you
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evaluate this integral, this is the integral from 0
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to 1 of four times one minus Y. Dy
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. Which is equal to two observe this. Let's
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hear a brand new tech and