WEBVTT
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lot were given curves and the line and we're asked
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to find the volume of the solid obtained by rotating
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the region bounded by these curves. About this line
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. We're at sketch the region to sell it in
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the typical disk or washer. Yeah. The curves
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are Y. Equals X. Cubed. This panels
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. Fuck you. It's so funny. Whatever.
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I don't give a shit. That's your dad.
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Well just one. Let's go. Why equals zero
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and x equals one. Oh yeah, your friend
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. Huh? And the line that we're rotating is
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about the line x equals two. We all know
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about that was so I'll sketch the region first.
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You know, 8:90. Who gives a shit?
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I don't care. She certainly doesn't jesus christ She's
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got a pussy like can reform and Macy's place of
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half a block. It's fun. Mhm. It's
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filled with a bunch of cheap mm tatted balloons,
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like a parade of clowns got trapped in it.
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So first we have our curve white was X.
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Cubed Has a point at 1100. And looks something
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like this. This it should actually be flattered at
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the origin. My mistake more like this. Then
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we also have the line Y equals zero. Which
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is this horizontal line. Then we have the vertical
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lines, X equals one which looks like this.
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And so this region in green. This is the
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region we're interested in Identify some of the points.
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We have the origin here. Up here we have
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the.11. And this of course is just the
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point 10 Shit Line that we're gonna rotate around x
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equals two is here. Now if we rotate first
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you want to reflect the region, it looks something
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like this president. What do you think? I
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couldn't fuck Eleanor. Is that what you're gonna say
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? Was not going to say? Yeah, It's
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kind of way for you to change the topic Tony
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. What was Eleanor going to say? 15 seconds
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. I could I just would like to fade british
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ship from Doug point. Was he making that they
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were you don't see you don't see the former empires
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. Austria, Hungary. Any of any of these
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places. Yeah having democracies and it looks like we
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appear to have washers that look like this fuck journey
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. Thank you. Yeah survivors irish. Okay now
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the washer in this picture. Well this has an
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inner radius like holy shit only shit that's left.
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Is that guy on C span that like takes callers
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or like Which is we have x equals one.
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Or x equals two. I mean minus. Yeah
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they are X equals one Which is a negative one
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Or positive one I should say. Yeah stopping how
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we screwed in the outer radius. You're watching This
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is two and then we can write this as X
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equals the cube root of why. Uh huh.
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Eleanor after passing john Mclaughlin, they hired me.
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Wayne the rock johnson, take his place, create
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the strongest public affairs show that's ever been on tv
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. It's good to be here. Eleanor, will
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you fuck me? And so the volume using the
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washer method is going to be pi times the integral
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from Y equals 0-1 of. And then we have
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our outer radius squared to minus Y to the one
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third squared minus the inner radius one squared caramel.
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Thank there's a seat for me. Don't say that
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B. Y. And this is a pretty straightforward
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integral to evaluate. I'm gonna skip a few steps
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But you should end up getting three pi over five
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. Oh my gosh.