5

Find the volume of the solid obtained by rotating the region enclosed by the graph of over the given interval about the linef() =*_ [-4,-21(Use symbolic notation an...

Question

Find the volume of the solid obtained by rotating the region enclosed by the graph of over the given interval about the linef() =*_ [-4,-21(Use symbolic notation and fractions where needed )Use the Shell Method t0 compute the volume of the solid obtained by rotating the region underneath the graph _ of y = over the interval [0,3], about(Use symbolic notation and fractions where needed )volume:

Find the volume of the solid obtained by rotating the region enclosed by the graph of over the given interval about the line f() =*_ [-4,-21 (Use symbolic notation and fractions where needed ) Use the Shell Method t0 compute the volume of the solid obtained by rotating the region underneath the graph _ of y = over the interval [0,3], about (Use symbolic notation and fractions where needed ) volume:



Answers

Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
$y=x, y=x e^{1-x / 2} ; \quad$ about $y=3$

So let's just get no graft Onda region and we want to rotate executed your ex military so will be with 123 So June 3 have inside between here and ah, Why Uncle to 60 Minutes Expo Far So? So we'd uh uh It looks like a backbone and facing down from 60. So we have to summon me 16 and we'll be freshening down against. And now we will have, uh, acting too and committed three Now why Coaches? They're awesome. But this region here may be the one we're looking for and we want to retain about why access. So for me, this one will be the exit on the of irritation. So you need to do this question. We had just placed the written into the Jew small regions here. 1st 1 in, uh, in the career. The 2nd 1 will be in being okay now because they're addition. Ah, access it. Could you? Why? So we had, uh, out of Rennes Cook too. From here. You're here. It's out of Randall's near and the Inner Rennes attitude. You echoed you? Yeah. So Volume Nico Jew. Bye. Ah, here. First we need to find this in the section as well. So you need to find into second Region it, Terry and ah! Ah! Where do you hear so many snuck three activity tree on Ben. Aah! Executed three. And the other one will have Ah, no lie. Excellent dreams. I was getting the Why would echo Jew 16 minus three. How far? So what you gonna go to? Ah, 16 minus dream off. I will be writing one. So we should get go to a 16 minutes 81. Could you? Minus 65. So this one will be sorry for the bat. Our intention here. But there's only coach in a minus 65 now. And now on the second front here will be We will know why. Echoed in 16. Minus ah. To how far? So we should get going too. Ah, 16 minus two above. Farm will be equal to the 16 coaches. Zero. So this bone him would be zero here. Okay, so it means dunder first. I think the better to trying again to make it nice now because this picture is not so nice. One start drawing again. So thanks. Yeah. 123 So we should have a bumble out will be 16 It with me here. So we have Joe run from only a Jew Jew on a wager here. Just you ugly here. Selling it. Draw again. Yeah, I know that. And Dan here executed three, actually. Ju ju on. Why I could you zero Why it could ju zero would be here and now That's Onley region. Then we're looking for him. I know what access. So it would be this region here. Is that jokes? Yeah. And now from here we have this Fuller this really? Here we go, Joe minus 65 and it's really good to zero. So now I know why goes from minus 65 on the way to zero and then we will have the out around us equal Jew isn't me out around us here and it's out the Radisson hey will be That comes our way Go Jew from the trigger on With which three in other writers were from here Julia and this in a rest It's my go to no function in terms of the under X So means that way it doesn't come to the ANC. Which again, huh? Ah, Expo for ego. Just 16 minus y so x. We go to your 60 months for our one of a far So it isn't B Ah! Hey, Go to the 16. Minus y. Our one of a fall. Okay, so now we're ready to find a room. Now out the runners in which three would be nice. Minus the Ina Radha's ico ju 60 minutes. Why a square and swam to rent a secret Jew. One of a Jew. Now, do I so got any good? You pie my 65 to 0 ni minus. Uh, hey, would you get in? Could you? Yeah. So it could be again. So I'm going to a planner Integral. Now, Gandhi and say, could you in the garden? I could unite. Why? Minus in the grub is one record, you know, 60 minus y half. You know, im, um out of three. With you, The vibe. A tree with Juli Tree. I'm still here, and the man is a warehouse. You're gonna bless. Now, limit goes from 1 65 to 0. So if we have bladder limit was get he called you. Ah, Bye. So ish again. A minus sign here, and, uh, it's better that you do it right? Here's where some miners will be out with the It will be minus by and now nine times minus 65 glass Do all the three 16 minus manners with me. The blast. 65 three hour Jew. Okay, now, every signifying this expression was getting good job by someone by on the nine. They go, Joe guy seven oven. I I'm on a skirt. A three. Yeah. So that was a fine Anderson. Yeah.

All right, So this question wants us to revolve the region bounded by the curve. Why equals 16 minus extra, the fourth and the lines X equals to an X equals three around the lie axis. So let's grab the curve so we can see what region we're dealing with. And it looks somewhat like this. So that means that this is our region. All right, so it wants us to graft this and then we're evolving this around the y axis. So since it's not touching the y axis, we have to use the washer method. So we have an outer and we have an inner radius. So our outer radius is well, that's just going to be the distance between zero and three, which is three. And our inner radius is going to be just half of why it's just the distance from the Y axis to this curve. And we wanted in terms of why, because that's the access were revolving around. So let's convert our function into that of why so 16 minus extra fourth equals. Why? So why minus 16 equals negative X to the fourth four 16 minus y equals X to the fourth or X equals square root. I'm sorry, the fourth room of 16 minus Why? And this is positive because our X values are positive. Okay, now we need to find our bounds. So we're looking for where? Why ranges? So we know ex ranges from 2 to 3. But where does why range? So if acts equals the square in 16 minus y we have two equals the fourth room of 16 minus why? And we know that two was the 4th 3rd or 16. So why equal zero there? And then for the 2nd 1 we have that three equals. It's the fourth through 16 minus why? And in this case, why equals negative 65 Because 65 plus 16 equals 81 which equals three to the fourth. So here are bounds and now we can set up our inner girl. Volume equals pi times the integral from negative 65 20 of our outer radius squared minus our inner radius squared. And we can just use the F in integrate function on the calculator to do this which is math than nine. And plugging this in, we find that our volume is for 25 over three times pi

So just get the craft of the jury questions. Thank you. Why? So now we were ahead. Execute your wife square. So we have some qualities Ana thinks it could. Just great guy. So maybe being on a gift? Yeah. So this will be scripted by this will be my square. And we need to find this intersection here. This well isn't gonna reach in them what you can from so Can't you find it? Intersection, We're gonna y square You could just kind of by and from here we can have waken square on both sides. So we have Why about for you go to why on we should have wise my phone minus one? Could you so and why? Why about three minus one? He could just zero So what? We could use a row. And why About which one is it? A blast that quite ankle June 1 This well so just never be one one funder. Why? And also one for the next. So now we should can't be able to fool Doesn't go be rotating about Uh no. Why access? So we should have another beast now hard. Do you want to sigh? Yeah, Hammond people taking. So now you have a room where he could you? We had you done that? No. Why? So we have from Joe to one that out. Uh uh. Radius. We're being this good wine. So I'm square that we have a wine minus in. The writers were being the Scranton White Square and we have scrammed out somewhere far. Do you want so good? Right? And now into girl. Why would your wife Scranton? Which you'll go right back out for B Y five b five? What is it? You want one? Always. Cuba minus one, almost five times Overby zone. So, having glad you five minus still be tree by over 10. There's a financing.

We are given curves into line and he has to find the volume of the solid obtained by rotating the region bounded by these curves. About this line. Were asked to sketch the region the solid in a typical disk or washer. The curves are Y equals X cubed. Okay, Y equals one. Index equals two. Right? And the line we're rotating is about the line Y equals -3. No, you say. Yeah. Where were you? Yes. So, first we'll sketch the region crisis is No. So yes. So first I'll sketch the cubic function bombs to sorry, has appointed the origin the inflection point where it's approximately flat and then increases like this. Right? Yeah. And we have a horizontal line. Y equals one go. Yeah. About here. Oh, so you're a sub, Does it sound like it? The line x equals two. No. Well this is this vertical line, Right. Mhm. This is going to be off the graph, but it's a pretty steep. Mhm. Uh All across frost steve region. It looks something like this. Have any uh I've got for this region. We want to figure out what some of these points are. For example, this point here is 1 1. This point here will it has the X coordinate of two and appears to have a wide coordinated as of one as well. This uh point up here. Well, we know it has annexed coordinative too, but we don't really know exactly what the why coordinate is. But if you plug in X equals two, we get Y equals eight. Awesome. He's got all that make The line going to rotate about is why equals -3. Look at they like spray. Get sprayed. Right? So this is our horizontal line. Y equals negative three. We're going to rotate around. It is very far down. And the guy, it almost doesn't even make sense to draw this graph. But so be it. Yes. Now I'll draw the solid as best as I can and blue first I'll outline the region and then I'm gonna reflect the region across the axis. Mm That's already yeah, here in new york research actually. Yes. Wait yeah, no, these guys who are HIV. Let's see. So it looks kind of like this 6000 square Yes, 6000 sq ft. Yeah, that are you one of those guys? Yeah, yeah, that do you think about? That's Yeah, I mean mhm. Would you give me a hand sure after the show? Yeah. Yes, Judah gala and what? Yeah, yeah, yeah. Dude impressions maybe you and joe list on Cleveland like yeah, they do a character. That's okay. I'm not sure. I can see the name. Look joe. I love that. I love that boy. Oh you have like ah it's the last oh just a baby. This baby girl. Was he a so it looks something like this? Please call Wendy lamb my vagina. This is where I'm a baby. A baby with a baby's person. I'm afraid the graph isn't going to help illustrate the surface very well or the solid. I mean, but it should be clear enough that we can tell This is actually the baby adults person. Uh there are washers. I can draw them in. Green ma'am. It's a girl and she has an adult's pussy, ma'am. I'm afraid to inform you your baby. Within that prosecute getting this. It's Mhm. What? Mm. I think what's called adam. Well down Judah shoot us. Right. That's me. Were pressed. Mm. System. Okay. He's just fucking shitting. Doesn't even know Adam. No. He's just going to do in spots. Yes. The gayest thing you've ever seen this comment? Yes. They have almost the same shaking and your kids. We haven't. What about a show Highlander in the cloud. He's second guys off throughout history and sometimes never chuck. Right. Sure. So it's hard to see. But there is this green washer and so we see that the washer has an inner radius questions. Doesn't doesn't highlight. He always. Which is one minus negative three, which is four. Yeah. And we have an outer radius right? Which is our function. Why equals X cubed minus negative three which is x cubed plus three. Let's wait. And therefore by the washer method are volume V is equal to pi times the integral From what we see. X ranges from 1-2. Mhm. Of our outside radius X square sorry X cubed plus three squared minus our inner radius. Four squared dx. This is a pretty easy integral to evaluate. You should be able to do it on your own, and once you do, you should get an answer. Let's see the of 471 pie over 14 pancreatic cancer.


Similar Solved Questions

5 answers
Motk Chspted 08 HalIEEAAL Prcaletan AFelrdmo Uf[Jolotnenuteic =rms i(4762AEiSmbinehMlnmttr ta LnpdnrHhec In Me , Dee4p 4d J 76 [ cAr garVnieft Wet ManFndereedontBetsCsterinoxaCarProbom
Motk Chspted 08 Hal IEEAAL Prcalet an A Felrdmo Uf[ Jolotne nuteic =rms i( 4762 AEi Smbineh Mlnmttr ta Ln pdnr Hhec In Me , Dee4p 4d J 76 [ cAr gar Vnieft Wet Man Fndereedont BetsC sterinox aCar Probom...
5 answers
-/7 POINTSAAT NOTESASA VOUR TEACHERsmall Bok globule has dlameter 0f 27 sconds arc Jnd 1000 pc from Eatth. What What this distance In AUs?dlameter ?
-/7 POINTS AAT NOTES ASA VOUR TEACHER small Bok globule has dlameter 0f 27 sconds arc Jnd 1000 pc from Eatth. What What this distance In AUs? dlameter ?...
5 answers
S1000 is invested in an account earning 3.2% annual interest compounded continuously: (a) Write the amount A(t) as function of time t (6) Calculate A(3) A(1) . What does this represent? A(3) A(1) (c) Calculate What does this represent? Al+h) A( (d) Calculate the diflerence quotient and simplily A4 much as possible: (e) What is the diflerence quotient when =1h=0.001? What does this represent?
S1000 is invested in an account earning 3.2% annual interest compounded continuously: (a) Write the amount A(t) as function of time t (6) Calculate A(3) A(1) . What does this represent? A(3) A(1) (c) Calculate What does this represent? Al+h) A( (d) Calculate the diflerence quotient and simplily A4 m...
5 answers
Calculate the pH of after 200.0 mLof 0.300 Macetic acid is titrated with 60.00 mL of 1.000 M NaOH?1.8 x 10 -51.a chemical equation showing neutralization reaction it in the net ionic form; YOU may exclude physical state2.a chemical equation showing any other chemical activity; you may exclude physical state7.0009.0544.9469.054.957.00
Calculate the pH of after 200.0 mLof 0.300 Macetic acid is titrated with 60.00 mL of 1.000 M NaOH? 1.8 x 10 -5 1.a chemical equation showing neutralization reaction it in the net ionic form; YOU may exclude physical state 2.a chemical equation showing any other chemical activity; you may exclude phy...
5 answers
A seclion of roller coaster is in (he shape of y = x" 6x2 + ax + 9. It is given thal at 1, the function y(1) attains its maximum value on the interval [0,2] Find the value ofa.A 1008 120C 140160Suppose that f() =t" St' + 9t? represent the amount of money in your bank account at time t Find the interval on which f (t) is concave down:(-o.o]lo,4 )(-44)
A seclion of roller coaster is in (he shape of y = x" 6x2 + ax + 9. It is given thal at 1, the function y(1) attains its maximum value on the interval [0,2] Find the value ofa. A 100 8 120 C 140 160 Suppose that f() =t" St' + 9t? represent the amount of money in your bank account at t...
1 answers
Solve each problem. (Assume that all items are equally priced.) Eight quarts of oil cost $\$ 14.00 .$ How much do 5 qt of oil cost?
Solve each problem. (Assume that all items are equally priced.) Eight quarts of oil cost $\$ 14.00 .$ How much do 5 qt of oil cost?...
5 answers
Thabest eynteb d ta beqagmokab:0 @ (ulj?-CHzHzSOaCH;ma Hz Pa(CHpCuu
Thabest eynteb d ta beqagmokab: 0 @ (ulj?-CHz HzSOa CH; ma Hz Pa (CHpCuu...
5 answers
The regression formula below, has wage level, Dummy variable has value of 1 for women ad 0 for men Y 0] +a,D+e; -1 n =0] ~n1- means the number of women and men, Use the least squares estimation formula 0z, induce to represent the difference average wages between men and womenC(Y-TJ(D _ D)(Hint: Ed; =n, ~Zdy -T, average wage of woman, ni=1C(D _ DJ?
the regression formula below, has wage level, Dummy variable has value of 1 for women ad 0 for men Y 0] +a,D+e; -1 n =0] ~n1- means the number of women and men, Use the least squares estimation formula 0z, induce to represent the difference average wages between men and women C(Y-TJ(D _ D) (Hint: ...
1 answers
Determine whether statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The first step in solving $\sqrt{x+6}=x+2$ is to square both sides, obtaining $x+6=x^{2}+4$
Determine whether statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The first step in solving $\sqrt{x+6}=x+2$ is to square both sides, obtaining $x+6=x^{2}+4$...
5 answers
Proteins The average molecular weight of an amino acid residue in a polypeptide is 110. What is the approximate molecular weight of the following proteins?a. Insulin (51 amino acids)b. Myosin (1750 amino acids)
Proteins The average molecular weight of an amino acid residue in a polypeptide is 110. What is the approximate molecular weight of the following proteins? a. Insulin (51 amino acids) b. Myosin (1750 amino acids)...
5 answers
Difcront sccondvoar moocalstudontshozonaldood Crosydtho sum ponicn The suslcl_ rjdinazlixtcd EclowCorgtvci DOdotidonun5numboiThe 6-number gunbrt is DO0Dwc ain m Ko (Use uscencing order Neqen= Jeoma: Dj notrourd ,"tich boiclot btbza (epieeentsPrete_Tnta
difcront sccondvoar moocalstudonts hozonal dood Crosy dtho sum ponicn The suslcl_ rjdinaz lixtcd Eclow Corgtvci DOdot idonun 5numboi The 6-number gunbrt is DO0Dwc ain m Ko (Use uscencing order Neqen= Jeoma: Dj notrourd , "tich boiclot btbza (epieeents Prete_Tnta...
5 answers
CoSuppose that p(c) = an*' converges 0n (~1, 1J, find the interval of n=u convergence of p(4r 1 (8left end included (enter Y or N):I =right end included (enter Y or NJ:to I =
Co Suppose that p(c) = an*' converges 0n (~1, 1J, find the interval of n=u convergence of p(4r 1 (8 left end included (enter Y or N): I = right end included (enter Y or NJ: to I =...
5 answers
The grzph 0i g consists to stralght Ilncs and semicircle: Useanswer the glven questions.(0} Flno the area beavecn thc graph and the X-axls over tne Interval [0,6]Tnls tha value of(D) Find the cnes between thc graph and thc *-axis on thc Interval [6, 18] and then multiply by mgativeFn the velueg(x)dx .(c) Ado your enswers Irom (0} @ndThls the value olg(x)ax ,o(rJaz ,
The grzph 0i g consists to stralght Ilncs and semicircle: Use answer the glven questions. (0} Flno the area beavecn thc graph and the X-axls over tne Interval [0,6] Tnls tha value of (D) Find the cnes between thc graph and thc *-axis on thc Interval [6, 18] and then multiply by mgative Fn the velue ...
5 answers
Problen 7.5Solve the simultanous System of twO COngruences (this means: write down al possible lues of _ ezthat satisfy both them at the same time):(mod 13) (mod '20)(Hixt : Solve tlue litstthcn substitute VOut ASWOTS into the Scconl.)Pwvof: AusWc" %oes here,
Problen 7.5 Solve the simultanous System of twO COngruences (this means: write down al possible lues of _ ezthat satisfy both them at the same time): (mod 13) (mod '20) (Hixt : Solve tlue litst thcn substitute VOut ASWOTS into the Scconl.) Pwvof: AusWc" %oes here,...

-- 0.019893--