WEBVTT
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Okay, This question Once a stir of all of
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the area underneath Weikel sine inverse X, where X
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is greater than zero around the y axis. So
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, with all volume of revolution questions, let's draw
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to see what we're dealing with. So Arc Sine
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has a domain from negative one No one. So
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if we're considering the positive side, we end at
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one here. And then if we graph park sign
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of X, it looks something like this, but
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we're evolving this area around the Y axis. So
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what we can do is convert this to a function
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of X and consider this area right here. And
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remember this Y value is pirate, too, because
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arc sine of one is pirates. So to convert
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to a function of acts, we could just see
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that sign of why equals X. So that becomes
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are integral. So are equals. Sign Why?
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So that means air volume is pi times the integral
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from zero to pi over too of sign of why
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squared d y and no, that's an integral that
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we can look up. Or at this point,
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you may have it memorized. So the integral of
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sine squared is 1/2 why minus 1/4 sign of two
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. Why? From 0 to 2. Pi Sorry
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, zero pi over too. And this becomes pi
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Times pi over two divided by two minus Well signed
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pie is zero minus 1/2 time. Zero minus 1/4
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time. Zero. So this is just equal to
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pi times pi over two divided by two, which
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is equal to high times over for or pi squared
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over for so that's our final answer.