WEBVTT
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in this exercise, we're being asked to look at
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this expression for a volume of a solid in integral
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form and describe the solid that is being the solid
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whose volume we are calculating. And the first thing
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that I noticed is the dX is giving me the
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width of individual slices. So I need to use
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the other two pieces to determine what shape the area
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of those slices are. Well, sine of X
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. Yeah is the only thing that's changing and sine
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of X is going to give me Going from 0
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to Pi. Just that sort of it will shape
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and it's being multiplied by a constant. So I've
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got something that is changing being multiplied by a constant
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, an individual value times a constant as an area
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. Two numbers being multiplied together to give me an
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area that's just a rectangle. So this is telling
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me that I've got rectangular slices. Mhm With an
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infinite decimal with delta X. And the one dimension
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of those slices is going is dependent on the X
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value and at zero it's going to be zero anywhere
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along the rest of the base. It's going to
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have a height that is given by that curve sign
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X. But the width is going to be a
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constant pi So if I have a slice there the
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way that will be pie. If I have a
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slice here, the width will be pie, I
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have a slice here 20 ft high. And if
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I have a slice at that end, the width
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will be pie. So what I have is a
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shape that has a rectangular base that has a width
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of pie and the length of pie. So it's
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actually a square base and it's being cut into rectangular
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slices. The height of the slices is given by
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the function sign over pie. The width of the
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slices is the width of the square pie. And
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what I've got overall is the square base here.
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The height is zero here, flight zero In the
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middle. The height is one and the shape of
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the face is making or the shape the height of
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the shape is making this sort of silo type sheep
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. Yeah, I can describe that verbally has oh
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a square base. This links hi and bring home
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parallel angular. It's like this make up the area
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. All right. All right. You spell directly
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of the 10 you were uh slices is given by
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X. X. Yeah. And that describes this
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shape mathematically visually. The shape has a square base
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and is making a silo shape. The ends of
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the silo are that sine of pi curve. So
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this total light is one is total with this pie
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. This total with this pie. This total with
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his pie. Uh huh.