refer-to-the-figure-and-find-the-volume-generated-by-rotating-the-given-region-about-the-specified-7

Question

Refer to the figure and find the volume generated by rotating the given region about the specified line.

$ \Re_2 $ about $ AB $

Amrita Bhasin · Accepted Answer

we know that in order to find the volume were integrating on the access parallel to the axis of rotation, you know, the axis of rotation is X equals one There for the outer radius is gonna be distance from X equals ear to the axis of rotation, which is one minus dear. We&#x27;re just simply one. And then we know the inner radius is gonna be the distance from why did the fourth equals X to the axis of rotation? X equals one. So again, using the same reasons. Which means we have one minus y to the fourth for the inner now, or volume is pi times integral from 01 of the inner. Okay, so what we just did is we reason the formula pi times outer minus inner and outer and inner. Both individuals scored so one squared is one. This is also squared. So we foiled us. So we So we took this which is the inner. And then we spend them when you square it. Then you use the foil method, right? So now we can simplify before we find the integral. We have to simplify this to go to y to the fourth minus wide of the eighth. Do you? Why now we can integrate. Use the power method, which means increased the experiment by one and divide by the new exponents. We have zero for the second bound of when we plug ins. Here we get zero, which means our solution is 13 point over 45.

Aparna Shakti · Answer

in this problem. It is asked that refer to the figure and find the volume generated by rotating the given region. About the specified line are too Mhm. About oh eight. Right? So Hill Washer method is used about by equals to zero. So let us let us take very simple method, right? Or to understand it. So how do we understand it? We will we want the volume generated by rotating the given. Right? So we are creating in this way. Right? So when it is related in this way that is about Y axis, right? So we can say that this is the area. Right? So all that area covered by we want for our two only. Right? So for getting her to we must take the whole area like this. Right? And the limits will be 10 to 14 X. Right from here. Because we are rotating in this way, this is about by access. So this will be work. The limit will be from 0-1. This we know. But for finding out the specified line are too right about the way we want our two regions. Right? So, if we want area for the art, so whole area that is we will be getting this is are we can see, we can assume it are right? So we know that if it is rotating, then the area becomes pi r squared. Right? So area covered with the pioneer square. And we will just integrated. So this week we want we will get the volume in this way. So the r value is fall for here. And after that you can see pirates square. Right? So this is subtracted, totally subtracted with this girl. Right? So the equation for this girl is why equals two for uh 4 to the Power four X to the Power one x 4. Right? So this is so if we subtract this we will get this reason right, isn&#x27;t it? So this is very easy. This becomes very easy here. Now we will see how to do so using washer method. This is called washing method in another. Thank you. So This is rotated around by equals to zero night. Remember about by a question jake. So now we can say volume will reward one. We equals two. Bye. Okay by equals to A. And that is B. Yeah, this is r squared minus I but it gets yeah. So here X equals to a Right equals to zero because we are We are having this limit. Right? So this limit is what this limit is 02 when you can see. So this is why equals to be Right. So y equals two. B is equal to that is you can say the limits need global immediately abandon it. You can say so in this way we will solve this. Now we becomes word. Now as I have already told that our square is four here, why equals to four. We will take Thanks. So we will right here like this. Bye. It should be mhm X equals to zero date. So here that this will be one And this will be 44 square This whole area with four. My question for discovered. So 4 -4 squared minus four eggs -1ra. The public one x 4 here expect So I think you have got why we&#x27;re doing this because from the whole area we are just subtracting this unwanted area because we want our two. Right? So no we becomes here after integration we will get bye 16 x minus 16 X. You can say when one by two plus one that is today by do divided right? Yeah. T B do only. Right. So here it will be limits. Exit question zero. This is what? Okay so this is very simple because we know that this formula is integration of facts to the power. Nd exist nothing but X to the power and plus one by N plus one plus C. That is our constant. This is very simple. So now where they&#x27;re moving we will just put the limit we will get bye 16 -325 today. Yeah. Right. And it will be minus the minus lower limit here. Mhm No it becomes life B. E question. Yeah. Bye pressure. But the aid -32 divided by today. That would be 16. Bye bye today here. Now we can easily say that this is the volume covered by the rotation about by Costa zero. You can say Yes The volume is 16. This will be 16. Bye bye three. Yeah. So here 16 Fiber three is in cuba Kunitz straight. Yeah. So it can also be Simplified with this. It becomes 16.755. Kill big your notes. So this is a answer to this problem. I hope you understood the concept. Thank you for watching.

Chris Trentman · Answer

were given a figure and the figure. A region in a specified line. We have to find the volume generated by rotating this region about this line. The region is. The region are too. Can you rotate about the line formed by Oc? Yeah. An 82 year old. Uh huh. Stickball baseball hat on sq. That way that so looking at the figure, there&#x27;s three parts. We have the curve. White holds one. You can be up or down. We have blue curve. The curve wife was the fourth root of X. Is a bound on the right and then we have victor&#x27;s superintendent. The vertical boundary x equals zero on the left group. Now O. C. Is the same as Uh huh. Here, is that the line X equals zero. This is the same as irritating about he Y axis Duke, I&#x27;m the Earl of this. And therefore looking at a figure, we get a disc take solid. And so we&#x27;ll use this method to find the volume. So we want to find the radius right away. It&#x27;s easy to see that the radius is simply Y equals the fourth root of X. Or instead not 45 X, but three years is X equals Why It&#x27;s A 4th. And so our volume by the disk method is the equals pi times the integral from Y equals 0 to 1 of our radius wide. The fourth square peg Dy. This isn&#x27;t easy to grow to evaluate. Once you do, you should get the answer. Hi over nine. That what

Chris Trentman · Answer

he was like he asked me for a dollar were given a figure in the figure. There&#x27;s a region of the line and we&#x27;re asked to find the volume generated by rotating this region about this line. The region is right. Our two rotating this about the line. BC. What I will give you some advice you know? Now do you know what pheromones are? I was like yeah. So looking at her figure, It sounded above by the line. Why it was one and bounded on the right ID occurred. Why equals the fourth root of X. And left by the line x equals zero. Now the line you see this is the horizontal line. Why it goes one three four. Looking at the figure, we see that we get a gift type solid. So that will use the best method. Therefore we need to find the radius of our disk. Ask jake. Well this is going to be y equals 1 -5 equals you fourth root of X. Um uh It&#x27;s bad. instead of volume. By the get method is high times and a girl from X equals zero two x equals one of the radius, one minus the fourth root of x squared. Yes, no, nothing you can say. And if you evaluate this in the role should get hi over 15.

Chris Trentman · Answer

trying to be were given a figure which contains a region in the line And rest to find the volume generated by rotating this region about this line. The region is R. three and we rotated about the line through a. D. It&#x27;s funny to watch, it&#x27;s Looking at the figure. It&#x27;s founded above. By the line. Like was a curb bike was the 4th root of X. Below. By the curve, Y equals X. And the line through A. B. Is the same as the line stand. Who got some X equals Y. You should just they should bring back our this is what did he like just for laughs or something. Problem. Notice that a routine about this line. You appear to get a washer type solid. So we&#x27;ll use the washer method now redefined the outside radius or outer radius. That&#x27;s what they fucking girls. So tell a company that this is equal to X equals one minus X equals Y. To the fourth. And the inner radius is one minus X equals Y. Like they all get the fuck. And by the washing method are volume B is pi times the integral from Y equals 0 to 1 of the outer radius, one minus Y to the fourth squared minus one minus Y in a radius square. Do you know why? Yeah, you? Re right. was literally just that I would say 20 after you evaluate this integral, you should get 17 pi over 45 addition. Okay, well I&#x27;m gonna stand up comedian.

Chris Trentman · Answer

it is were given a figure which contains a region and a line can rest to find the volume generated by rotating this region about this line. The region is are one and the line of a rotating about is the line formed by a bee. So looking at the figure, maybe you talk me that way. I you talked me well we rotate the roads hitting about the line. Yes X equals one and therefore what we get is not a washer. Walk here, simply a gift. We&#x27;re using this method. You laugh. Yeah. One of you. Yeah. Funny. How funny. Right. Crown. So you want to find the radius. Funny how from a figure she had the radius? Yes one minus uh X equals y. Radius is one minus Y. And therefore using the this method the volume is high times the integral from why equals zero. So y equals one of the radius one minus y squared. See why this is a pretty simple integral to evaluate. Once you do, you should get the answer. Hi, over three.

Amrita Bhasin · Answer

it&#x27;s a problem to problem is referred to the bigger and find the volume generated by painting keeping region about suspensive are aligned I chew about a b r to is this region on? Did this curve is why you called to ax to our force A B is a vertical line Now if we rotate this region about a B then oh, it&#x27;s line we can see the cross section is the washer ways in their wild years one minus Why? To force and out your values one. Now we have the wild way is the coach You high times into girl from zero to one one squared minus one minus wise to force going He wants so justice because your pie into girl from zero to one one minus Why? To force minus one square B Why So this is a call to a pine into girl from there once one minus live to paint menace to live to warm us Want you want This is a cultural pie Integral found zero one to lie to force Honest What shoot? Paragraph eight you are This is a cultural hi two times two over five Why two five minus one over nine. One, two, nine from zero to what? His answer is high times to over five, minus one over nine. This this come true. They&#x27;re keen pie o r forty five.

Amrita Bhasin · Answer

uh for giving a figure which consume the region and you&#x27;re lying and rest defying the volume generated by rotating it. This region about this line, the region is are too. And we&#x27;re lab rotating it about the line. Baby man looking at the figure where he&#x27;s just like, well you have the upper bound on the region. Why equals 12 bound on the side on the right side. Should say is X equals uh Why he goes the 4th root of X. And you know, bounds. No, it&#x27;s not. The bound on the left hand side is just X equals zero. And if we&#x27;re rotating about a B, This is the same as rotating about the line x equals one. Yeah, he has a pit bull to and with human arm. Now looking at a figure, it&#x27;s clear that we will get a washer type solid that we use the washer method About 100 lb. So we need to find the radius radi I of the washer. Yeah, we&#x27;re looking at the figure. It appears that the outer radius of the washer with one and the inner radius to sort of is X equals one minus X equals y. Before and so using the washer method, the volume is equal to high times integral. From y equals zero to y equals one of the outer radius, one squared minus the inner radius one minus y to the fourth squared Dy They get to a certain age where they&#x27;re like, well I guess I&#x27;m smart now. I guess I&#x27;ve smart years old. Yeah. And this is a pretty easy integral to evaluate. Once you do, you should get 13 pie. Talk to the judge all Over 45 10 guys sit there please.

Problem

Refer to the figure and find the volume generated…

Problem 25 Hard Difficulty

Refer to the figure and find the volume generated by rotating the given region about the specified line.

$ \Re_2 $ about $ AB $

Answer

$\frac{13}{45} \pi$

More Answers

Related Courses

Calculus

Related Topics

Discussion

Top Calculus 2 / BC Educators

Catherine R.

Heather Z.

Kristen K.

Michael J.

Calculus 2 / BC Courses

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 6

Video Transcript

James Stewart

Calculus

Catherine R.

Heather Z.

Kristen K.

Michael J.

Integration Review - Intro

Definite vs Indefinite

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\frac{13}{45} \pi$

Calculus

Catherine R.

Heather Z.

Kristen K.

Michael J.

Integration Review - Intro

Definite vs Indefinite

James StewartCalculus

Catherine R.

Heather Z.

Kristen K.

Michael J.

James Stewart

Calculus