WEBVTT
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we were given curves. We'll have to find use
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a graph to find the approximate X coordinates of the
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points of intersection of these curves. Then rescues are
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calculated to find approximately the volume of the salt obtained
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by rotating about the X. Axis. The region
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bounded by these curves. The curbs are Y equals
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one plus X times E. To the negative X
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. Cubed. Yeah. Then all the and why
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equals arc tangent of X squared. Got a new
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pitch next to a tiny microwave and warming up but
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really just suck on your other. So first I'll
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use Dismas online graphing calculator to graph these curves and
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to find the points of intersection. Right. Sure
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. It's a trap. So here is the graph
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of the curves. The graph appears to have what
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we see two points of intersection here and here.
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The point of intersection on the left. This has
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X coordinate about negative 57 Any second X coordinate on
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the right. The point of intersection is about 1.391
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. You are supposed to have more? She's right
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. But so it's a catered event shot. No
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. Now if you wrote this about the X axis
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, we're going to have to use the washer method
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for our washers. The outer radius. The analyst
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type is the top function which is one plus X
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times E. To the negative X cubed. Break
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out of your. Yeah. And the inner radius
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was maybe they say oh did you? And groceries
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channels Z equal to arc tangent of X squared.
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It's a bit of a like a little treat as
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everyone knows. And so by the washer method,
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the volume of the rotated region. The solid is
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pi times the integral from the left X X 1
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to the right x coordinate X two of our outer
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radius one plus X. E. To the negative
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X cubed squared minus the inner radius arc tangent of
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X squared squared dx. This is a complicated volume
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, but if you use a calculator, you should
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find this is approximately key does of only your own
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son, but it 6.9234 less than on sunday.
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There are more safe. Okay, But so in
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your ass.