5

Find the volume of the solid obtained by rotating the regionbounded by y=x2+1, x=1, x=7, and y=5 around they-axis using washers. would you have to get the equation ...

Question

Find the volume of the solid obtained by rotating the regionbounded by y=x2+1, x=1, x=7, and y=5 around they-axis using washers. would you have to get the equation in termsof x?

Find the volume of the solid obtained by rotating the region bounded by y=x2+1, x=1, x=7, and y=5 around the y-axis using washers. would you have to get the equation in terms of x?



Answers

Find the volume of the solid obtained by rotating about the
$x$ -axis the region bounded by the curves $y=e^{x}, y=0$
$x=0,$ and $x=1$

In the question we have to find the volume of a solid obtained by rotating about by excess. And the region bounded by the curves by school. Three to the power minus x square by schools to zero X is close to zero and excess calls to one. Now moving towards the solution here, rotating about the y axis. The cylindrical shell method will be simpler. So like the height equal to E. To the power minus X. Two minus x square. So the radius will be equal to R. S equals two weeks which goes from 0 to 1. So we will be equal to integral of two by R H. D. X. That is we will be called to to buy into integration from 0 to 1 X into E. To the power minus X square D. X. Now we will be solving this integral. So let you be equal to minus x square and then do you will be equal to minus two X. Dx. That is minus one by two D. You will be equal to x dx. So putting these values you will get your limit going from a equals two minus x square to minus zero square that is zero and we will be from minus one square that is minus. But so the integral will be Dubai into Integration from 0 to -1 -1 by two E. To the power you do you Solving This? You will get -9 E to the power you limit going from 0 to -1. That is minus phi into each of the power minus one minus one. Solving this. You will get your answer approximately equal to 1.986 Thank you.

All right, So this question wants us to revolve the area between these two curves around the line. Why equals 15? So let's do a rough sketch. We have our and then we have a line over here, you know, once here in the first quadrant. So this is our region, and we're evolving and around. Why equals 15 which, for simplicity's sake, let's just put that up here. It's not to scale. So since this line and region is not touching, why equals 15? We have to use the washer method. So first, let's draw outer idiots. So we see here that are, oh equals top minus bottom 15 minus the red curve, which is X squared and then are inter radius equals top minus the bottom, which in this case, is the line. So no, we confined our volume. Volume equals the integral from zero to our intersection point, which we confined real quick by setting the two equal to each other. X squared equals 12 minus acts. Then collect all of it one side product of negative 12 some of one that would be X plus for times X minus three. So X equals negative for and X equals positive. Three. So which one of those do we want? Well, this intersection is in the positive X. So we want positive three Integral from 0 to 3 of our outer radius squared, which is X squared. No, just 15 minus x square. Quantity squared minus our inner radius squared, which is 15 minus 12 minus x squared. This is all district acts and that simplifies Thio 1953 over five. Hi.

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.

So let's just get the region that we want to rotate about. Execute humanist you. So no only way to know tonight. So why I could just great the juice from the banks So And when he looks like this one? No. Why did you act? So will be another line. You know Andi and this region here when he looks that is so. We need to find us in this section here. So you find in detection we move them ico So juice Quinto Thanks Echoed your thanks. So we shouldn't get square on both. Side was against it for x x, X square. So addition means that X squared minus far Thank you could just go. Thanks. Thanks Minus far It got user So Anchorages on Execute your phone So it is Don't be far. It would've from him on another phone here for that. Why? And we want you today about the lie expert You Minister Exit Minister will be Yeah So just lie would be accepted you Minister to a little thing like this one So we need to find the outer Rangers would be this one without the writers here on image of communities out the reddest hair would be It can tow, huh? You Could you Ah, here we have No ah, the function in terms of doing when and on da Ah, I under wise I was confined out isn't as ah angst. We go Jew y square. I'm a far Anderson execute you. Why? So what should be and what you write down is Rinus Here you go to ah isn't being. Why and we bless in Underland. Here will be two. I want a readiness for the inner runners way we will have from here on the way to here, you know? So we have this my our ego Jew Onda function being white square minus far. So why square I'll do every far and were blessing undervalued to here. Okay, so now we're ready to find, uh, room you go to Now the wind goes from zero to far. Buy out the riders in Could you wireless too? And then we put a square minus the inner Radisson Could you wise Square? And even before this shoe, it was square day. Why? So we should get going to buy you too far. Why? Square bliss for a while was far miners and we should get ink or Joe on weeping the fall We can do like ah, why off almost 16 and then remind us fall times One of probably one with two times two will be Once it would be quite square here. And we'll be minus far knew why It's about Majid bhai. I don't need you far. So we've got minus wife. Almost 16 so far the white square we can someone the White Square and now fund Why we're gonna breast for Why follow? Concerned whether man is far So we got only days. Do you know why go to buy so in the court Isn't he called you minus? Why about five divided by five time 16 you Could you go, Joe? I ate the and now blast to Why square then? It goes from there too far. So what you're getting good bye. All right for my fight. So Inbee for about five will be, uh too Oh, uh Juba Jules Fr mama June being a uh huh uh Well, fine. We'll beat you. Powered job finds you gonna to about 10. Joe Barton will be 10 Jenny far. So you go, Joe minus 10 don't you fall on your mind Ah, the I know times two okay. And then we plus ah, we have have false crown Will be 16 16 comes to I will be affected too So we got 10 gente far the environment a d you got in cold Jew trolley vomit And so be, uh, one gente I remember 10. All right, last 22. Come on. That's yeah. So my uncle did you leave? I met you on ma. So you got my message. Ah city Far. 05 Plus that did you. So we got it going to buy it. Maybe five minus 64 rust that June Times five Bennett 1 60 So the final answer will be 1 16 minus 64 Gonna night these six by five


Similar Solved Questions

5 answers
Pt) Evaluate the integral.Vg-xzVg-xz-zzdy dz dx = Vg-xz-zz (x2 +y + 22)1/2V9-xz
pt) Evaluate the integral. Vg-xz Vg-xz-zz dy dz dx = Vg-xz-zz (x2 +y + 22)1/2 V9-xz...
5 answers
Problem 4. Prove thatN = {id,(12)(34),(13)(24),(14)(23)} € S4is a normal subgroup_
Problem 4. Prove that N = {id,(12)(34),(13)(24),(14)(23)} € S4 is a normal subgroup_...
5 answers
-/1.66 pointsConsider the parametric eouatons Yaclont cos(t) t sintc), 3 [ < 7/3 Kneqr that represents (hc area surface obta nedStt UProtating tne given curve about tnc Y-axis-71,7 points SCalcET8 10.2.513.XPaFind tne @lacthe surace ohtalned foleting trn given cuive Juduttho *Jris
-/1.66 points Consider the parametric eouatons Yaclon t cos(t) t sintc), 3 [ < 7/3 Kneqr that represents (hc area surface obta ned Stt UP rotating tne given curve about tnc Y-axis -71,7 points SCalcET8 10.2.513.XPa Find tne @lac the surace ohtalned foleting trn given cuive Juduttho *Jris...
5 answers
1 . Calculate the formula masses of the following compounds: calcium hydrogen sulfite, magnesium phosphate, Iithium carbonate , glycerol, glucose, caffeine.How many moles of water contain 3.28 x 1024 molecules of water?
1 . Calculate the formula masses of the following compounds: calcium hydrogen sulfite, magnesium phosphate, Iithium carbonate , glycerol, glucose, caffeine. How many moles of water contain 3.28 x 1024 molecules of water?...
5 answers
Number Systems and the Complement Method for Negative NumbersNumber Systems In what base is the following operation performed:ABC + CBA = 1443ii. Show how to represent the numbers (A3 1) and (A3 + 1) as base eleven numbers_ jii. Show how to represent (b" _ 1) and (6" + 1) as base b numbers, where b can be any integer larger than 1 and n any integer larger than 0.
Number Systems and the Complement Method for Negative Numbers Number Systems In what base is the following operation performed: ABC + CBA = 1443 ii. Show how to represent the numbers (A3 1) and (A3 + 1) as base eleven numbers_ jii. Show how to represent (b" _ 1) and (6" + 1) as base b numb...
5 answers
) The capacitor in the RC circuit shown below is initially uncharged The switch is closed at t= 0s. t=0 3.6kn 15V 27uFa.[3 points] The time constant for this circuit is 6.[5 points] Calculate the time it takes for the electric potential across the capacitor to build up to 8 V
) The capacitor in the RC circuit shown below is initially uncharged The switch is closed at t= 0s. t=0 3.6kn 15V 27uF a.[3 points] The time constant for this circuit is 6.[5 points] Calculate the time it takes for the electric potential across the capacitor to build up to 8 V...
2 answers
Give the following compounds the IUPAC namesCH_Ol13CHCHCH CH C CH14CzC Bt15
Give the following compounds the IUPAC names CH_ Ol 13 CHCHCH CH C CH 14 CzC Bt 15...
5 answers
Quesdon 17 01 18 point) Attempl 1 o UnlimifedSolve for 9. Express your answer in simplest and exact fom_for q > 0
Quesdon 17 01 18 point) Attempl 1 o Unlimifed Solve for 9. Express your answer in simplest and exact fom_ for q > 0...
5 answers
To tcst thc scriosconvergence, YOU will use the Limit Comparison Test, comparingI0X" 3KIIto the senesJk wncrc P
To tcst thc scrios convergence, YOU will use the Limit Comparison Test, comparing I0X" 3KII to the senes Jk wncrc P...
5 answers
Write a system of equations and solve.Find two numbers whose product is 28 and whose sum is 11.
Write a system of equations and solve. Find two numbers whose product is 28 and whose sum is 11....
1 answers
(Continuation of Example $1 .$ ) Graph the functions $f(x)=\sqrt{x}$ and $g(x)=\sqrt{1-x}$ together with their (a) sum, (b) product, (c) two differences, (d) two quotients.
(Continuation of Example $1 .$ ) Graph the functions $f(x)=\sqrt{x}$ and $g(x)=\sqrt{1-x}$ together with their (a) sum, (b) product, (c) two differences, (d) two quotients....
5 answers
The major biological process that makes nitrogen available to plants is Nitrogen fixation carried out by soil microarthropods Nitrogen fixation carried out by mycorrhizal fungi C, Nitrogen fixation which occurs abiotically and converts nitrate t0 nitrogen gas Nitrogen fixation carried out by soil and plant symbiotic bacteria
The major biological process that makes nitrogen available to plants is Nitrogen fixation carried out by soil microarthropods Nitrogen fixation carried out by mycorrhizal fungi C, Nitrogen fixation which occurs abiotically and converts nitrate t0 nitrogen gas Nitrogen fixation carried out by soil an...
5 answers
Simplify the following 9!6!9!6! = (n+9)!(n+8)!(n+9)!(n+8)! = (n−1)!(n+1)!(n-1)!(n+1)! = n!n(n−1)!n!n(n-1)! =
Simplify the following 9!6!9!6! = (n+9)!(n+8)!(n+9)!(n+8)! = (n−1)!(n+1)!(n-1)!(n+1)! = n!n(n−1)!n!n(n-1)! =...
5 answers
Find the radius of convergence of the following series 0O (nu)? Sxn+6 n=1 3" (2n)lThe radius of convergence is (Simplify your answer:)
Find the radius of convergence of the following series 0O (nu)? Sxn+6 n=1 3" (2n)l The radius of convergence is (Simplify your answer:)...
5 answers
Find the mode, median, range and interquartile range for thefollowing data given as a stem-and-leafdiagram with stem unit = 100.Stem Leaves10 8 2211 8 2 2612 2 5613 8 5
Find the mode, median, range and interquartile range for the following data given as a stem-and-leaf diagram with stem unit = 100. Stem Leaves 10 8 2 2 11 8 2 2 6 12 2 5 6 13 8 5...
5 answers
Consider rhe funcrion41)Write out che sum cf the hirst non zero terms of the MacLaurin series for the function_6) "Use pan a) to write che sum ofche firit non zero terms of che FacLaurin series for2_1 Ma; = 1, S0) =0Suoni80278
Consider rhe funcrion 41) Write out che sum cf the hirst non zero terms of the MacLaurin series for the function_ 6) "Use pan a) to write che sum ofche firit non zero terms of che FacLaurin series for 2_1 Ma; = 1, S0) =0 Suoni80278...

-- 0.023247--