WEBVTT
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in this problem. It is asked that refer to
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the figure and find the volume generated by rotating the
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given region. About the specified line are too Mhm
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. About oh eight. Right? So Hill Washer
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method is used about by equals to zero. So
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let us let us take very simple method, right
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? Or to understand it. So how do we
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understand it? We will we want the volume generated
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by rotating the given. Right? So we are
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creating in this way. Right? So when it
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is related in this way that is about Y axis
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, right? So we can say that this is
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the area. Right? So all that area covered
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by we want for our two only. Right?
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So for getting her to we must take the whole
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area like this. Right? And the limits will
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be 10 to 14 X. Right from here.
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Because we are rotating in this way, this is
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about by access. So this will be work.
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The limit will be from 0-1. This we know
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. But for finding out the specified line are too
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right about the way we want our two regions.
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Right? So, if we want area for the
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art, so whole area that is we will be
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getting this is are we can see, we can
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assume it are right? So we know that if
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it is rotating, then the area becomes pi r
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squared. Right? So area covered with the pioneer
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square. And we will just integrated. So this
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week we want we will get the volume in this
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way. So the r value is fall for here
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. And after that you can see pirates square.
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Right? So this is subtracted, totally subtracted with
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this girl. Right? So the equation for this
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girl is why equals two for uh 4 to the
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Power four X to the Power one x 4.
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Right? So this is so if we subtract this
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we will get this reason right, isn't it?
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So this is very easy. This becomes very easy
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here. Now we will see how to do so
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using washer method. This is called washing method in
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another. Thank you. So This is rotated around
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by equals to zero night. Remember about by a
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question jake. So now we can say volume will
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reward one. We equals two. Bye. Okay
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by equals to A. And that is B.
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Yeah, this is r squared minus I but it
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gets yeah. So here X equals to a Right
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equals to zero because we are We are having this
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limit. Right? So this limit is what this
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limit is 02 when you can see. So this
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is why equals to be Right. So y equals
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two. B is equal to that is you can
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say the limits need global immediately abandon it. You
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can say so in this way we will solve this
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. Now we becomes word. Now as I have
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already told that our square is four here, why
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equals to four. We will take Thanks. So
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we will right here like this. Bye. It
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should be mhm X equals to zero date. So
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here that this will be one And this will be
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44 square This whole area with four. My question
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for discovered. So 4-4 squared minus four eggs
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-1ra. The public one x 4 here expect So
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I think you have got why we're doing this because
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from the whole area we are just subtracting this unwanted
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area because we want our two. Right? So
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no we becomes here after integration we will get bye
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16 x minus 16 X. You can say when
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one by two plus one that is today by do
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divided right? Yeah. T B do only.
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Right. So here it will be limits. Exit
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question zero. This is what? Okay so this
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is very simple because we know that this formula is
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integration of facts to the power. Nd exist nothing
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but X to the power and plus one by N
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plus one plus C. That is our constant.
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This is very simple. So now where they're moving
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we will just put the limit we will get bye
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16-325 today. Yeah. Right. And it
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will be minus the minus lower limit here. Mhm
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No it becomes life B. E question. Yeah
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. Bye pressure. But the aid-32 divided by
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today. That would be 16. Bye bye today
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here. Now we can easily say that this is
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the volume covered by the rotation about by Costa zero
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. You can say Yes The volume is 16.
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This will be 16. Bye bye three. Yeah
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. So here 16 Fiber three is in cuba Kunitz
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straight. Yeah. So it can also be Simplified
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with this. It becomes 16.755. Kill big your
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notes. So this is a answer to this problem
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. I hope you understood the concept. Thank you
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for watching.