5

Find the volume generated by revolving the region bounded by y lnx +2 y = and y Sketch the region _about the lineb) Suppose that f is continuous [unetion Such that ...

Question

Find the volume generated by revolving the region bounded by y lnx +2 y = and y Sketch the region _about the lineb) Suppose that f is continuous [unetion Such that f () =cf f(dt _ +r3 for all and f (a) = for some real muIber Find f' (a) in terIns 0f Only.

Find the volume generated by revolving the region bounded by y lnx +2 y = and y Sketch the region _ about the line b) Suppose that f is continuous [unetion Such that f () =cf f(dt _ +r3 for all and f (a) = for some real muIber Find f' (a) in terIns 0f Only.



Answers

Find the volume generated by revolving the region under the graph about the $y$ -axis. $$f(x)=x e^{x}, \quad x \in[0,1]$$

This question asks us to find the volume off the service of her revolution. Uh, defined by FX is X that in the mix, um, between, uh, zero x and two on We're saying zero for X equals zero and we take the service of evolution around the X axis. So, um, in an earlier question, I think it was a question. Ah, well, let's see, it was question 67. I went through sort of the formulas for surfaces of revolution or, um, volumes of revolution. Uh, so for this case or functions like this one, two, zero, Um, and the volume for X is the integral from zero to of five times x squared and the next it's weird. The ex. Now, this is a tricky question because there is something going on at zero. That's not quite clear. Um, but you can check. It's probably a question hat were were first on the limit. The limit off excellent X as X goes to zero, actually is zero. So there's this is no actually an improper integral. This is a perfectly fine, integral, uh, so we can just do it. Uh, even there's no super easy. I think the easiest solution will be to do integration by parts considering X squared is derivative and Adam of excess not yet derivative. That would mean that this becomes flight times 1/3 X cubes and then of X squared between zero and two, minus the integral from zero to off, huh? By times 1/3 execute Now, times the derivative off an X squared, which will be by Jane rule. It will be one over X times two in the next DX. So we do see, we have simplified things a little bit, Um, so plugging in zero to dysfunction, uh, by the mission field zero. So that one of ashes that we do get the by times ace divided by three. That oughta do squared. Ah, and then this integral, which is minus by integral from 0 to 2. So we get 2/3 X squared, all of X, the ex and basically we're just going to repeat this procedure so we'll continue over here. We have in thirds long do squared minus bye. So in this, games were fueling 2/3 square as the thing we are, um uh, integrating basically. So we get something with X cubed So we should have to ninth. Because if we do that by most by that by three, we get 2/3 at times. Other vics zero and two, uh, minus the integral from 0 to 2. So we have the, uh, to ninth. Thanks. Cubes, Uh, in a dirigible that next, which is one over X, the eggs. So that's just simple politeness in here. This is X squared. Okay, so now we have a bunch of things that are administrate for two integrates. So this is and two squared minus body times. Um, living in zero again. Yields zero. So we got, uh, two divided by nine times eight's, Ellen. Too minus. Um, So this time we get to divided by 27 x cubes between zero and two. So the final answer, which is no, a nice expression at all. This a by over three long do squared minus ah, 16 pi over nine. Long too. Plus, um, let's see what that would become. That would be, like 60. Number 27 16 by over 27. Yes, we put in the 20 again, you zero. So that would be your final answer. Now, I assume I didn't see it in the book, but I'd expect if you get a question like this, it actually wants you to do this using a graphing utility and you'll get, um, some nice. Uh, what specific number? I think this is approximately two. Um, but you should check this. So whether shows that you can do this by hand, But I suspects that this question, um, should have stayed in somewhere to use your graphing utility because it's the answer is just very complicated.

In discussion we have a function Fx recalls to access where opponent the route 1- x esquire we need to draw the graph for the function F. There's the whole the whole discussion the graph of the function F is shown below so this is the graph for the function F. Now let's move to part B. We need to find the idea between the graph of F and G. Xx is from access equals to zero to access vehicles to one by two to find the area We can write a because to integration they do one x 2 access square upon Underwood one minus X esquire dx to solve this integration consider x equals two sign you therefore by the differentiation we can right Do you have three calls to because I knew do you now substitute Access equals to zero so we get Using close to zero and when we substitute Access equals 2 1 x two we get you with close to by by six hands The above integration completeness area is equals two 02 by by six science where you were born on the road one minus sine esquire you because I knew do you this will be cause to integration that will do by bicycle Sinus choir you upon one minus sine squared you this will be called to cosign Squire you and the under root of course any square you will be called to of course I knew and two because I knew do you this cause I knew will be cancelled with the because I knew hence we get Integration we go to five x 6 Sinus choir you do you we know that Cosine Theta is equal to 1 -1 to Sinus choir tita hands The values and its creditors will be called to 1 -1 co sign two hitter upon to so special this value in the our integration so the idea becomes a vehicles to integration zero to Pi by six one x 2 because I do you upon to do you and this will be calls to one by today you will be called to You buy two because I into you up onto this will be calls to sign Do you upon four and the limits are 02 by by six Now many substitutes are limits we get area A because to two by minus three rules 3 upon 24 so this is the answer for the area another small to part C in part C we need to find the volume of the solar generated by devolving area about the Y axis to redeem described in the part B So the expression to calculate or the formula to calculate volume is formed by vehicles to integration X one that works too bye affect the Squire dx substitute all the values so we get volume vehicles to integration 021 x two by esquire upon one minus X esquire D X. Now we are going to play the same matter we consider X equals two sign you hands do you have physicals too because I knew the U and the limits becomes when excess goes to zero use goes to zero and when access goes to one x 2 you becomes five x 6 and We can written as vehicles to 02 by by six bye signed to the power for you upon because science choir you into because i knew do you so the Sylvia calls to by integration 0 to 5 x six signed to the power for you upon because I knew do you now first of all simplify this expression so we can write by integration will to buy by six saying Squire you into Sinus square you upon of course I knew do you so this will be calls to by integration deal to buy by six sign is where you and we can write Sinus Choir You as one because science choir you upon of course i knew do you there will be calls to By integration will do five x 6 fine square U minus scientists where you because I mean square you upon because i knew do you This will be caused to by integration YouTube by by six again apply Sinus quarter Tabasco tennis court it has close to one so we can write Sinus square us one minus because i inspired you minus Sinus square you because I inspire you upon because I knew in two d U so this will be equals two by integration will to pie by six he can't U minus because I knew minus Sinus choir you because I knew do you Another expression has been simplified and now we can find the integration of this expression so the integration will be bye the integration of security do you can Britain is log second you plus 10 gently you minus the integration. Of course I knew that you will be called to sign you minus the integration of Sinus square because I know you will be close to one up on three thank you for you and the limits are 0 to five by six no society or the limits so we get bye log 2nd 5 x six plus 10.5 x six Yeah sign Bye bye 6 -1 up on three Sign Q by by six minus bye log see candiru plus 10 Jan 0 0 signed 0 -1 upon three thank you. Zero And when we for this Albert finally we get volume v equals two five log rule three miners 13.24 so this is the final answer for this problem. I hope you understand the solution. Thank you

We have different parts of the question. Each other box in this army. The area. So what's the problem? You define idiotic? It is tradition off one movie in the next days. So did you deny us It s not one my last? Because you know himself in the last into the early years. What news? This is your goodness. Internet minus giving off whenever. The next day. So it is. He denies x the next mass six Want with me, You can ask the Ellen B minus the minus one. Ellen, the Genesis e in the A minus. It is judo class in my life played last one, which is equal. You'll be what, Beyond the way finding by being the problem. Yes. Well, well, okay. Hey, Anderson. Things you're finding it is and what is black? You want me when we buy Internet days? No, this is given as bye. Well, it Well, this is You didn't do Internet this well, it's no big deal, you know. Do you want internet for this? Well, you do love. There's worse things. Is it enough? Okay. And go nn What is? Well, my guess is enough. So whenever x x be it. Is it tonight? It is. It is what it is, but minus lies because no LF days, you know, doom. It was minus toe do. And the limits? No, we have this for the mass. Bye. A what? Minus doing E my well, then when? Well, it's my best, will you? Well, anyone? This is Julia is the guns do a minus minus. Do you mind doing man into a minus? It's because minus he might ask you This is dancer part B of the problem. Now we have a sea of the problem. We're finding the one. So this is given us one. He was by one movie. Exp less do and then ask. What is it, Ellen? It is not express to the X minus. There's no on the top and it s it's enough. It's plus toe the X order beings visited and the next and do it well. But less. Yes, my name is No. You know what ISS? Thank you. And it's why maybe less. Authorities. You know what? That So I'm thinking he had This s Ellen s. You think a swell, my food Bless. Here's mine. It's you know no one of us. You do X into X one class. Yes, it's Kansas. Each other definitely becomes in a minute. Do it is one who bless you. It's my ass. You know you're blessed. Extra one rule dues, not This becomes. And then if you do, it's just a mess. Is my yes less 10 room. And me you do is, well. One. Who? Yes, being a minus. Wait, That's one of 14 year span. Minus hit. Anyone? You do have less to do. Minus Yes. One of 1/4 of the lens. He's just given us it. Let me do. Yes. Why would mess way minus? Yes. What a fool. Minus do the math lesson about fools. Not just guns. Yes, we're going to do less to minus two minus four. That's mine. Give enough. Who is minus? That's an anagram. He's got a phone call. That's manna form. Well, given anyone a bump or anything about last night, this is, uh, well for the division. Now you want it was the violent one of four. Will do. Yes, but this man just you can add. Why do you do it? So this is that warning. Did that box. Not in the bottom of the of the question. If your plan Cento which is expert why so its body place? Because, you know, one day the next there's this is it Internet? It's in my body. Huh? Listen, I want you in the next. What is that? Mr. Farr? We're going down. It's Bob. Does it matter? In an instant The X squad do my national rex. It is by a bamboo BX. You can ask because I do. And this it is one of my team one. The limbs begin as yes, Ellen E minus 1.4 is fire minus. Now this is you can do. Yes, and sort of This is one for you. Minus. Is God going full? Blast 14 One of one would do. Yes, but less. We have x by this. No, we have to go. Why buy? Because peace again as what? A horrible in finishing off Internet. What it's gotta be. It's This is your demands. Uh, this isn't our be. We have a beautiful for me Internet. What? It's gonna be x you best in my school. Therefore we have my back because when I'm going through the minds, too. This is dancer. Deal the problem. We have ancestral, gay B, C and D of the problem there before this system ornaments.

In discussion we need to find the volume generated by devolving the region under the graph about Y axis and the human function is FX is equals two ex Synnex and the limits are zero to buy. Let's see how to solve this question. We know that the formula to calculate the volume is given by integration. It will be to my ex f x D X substitute the limits and the function in this formula we get vehicles to zero to pi to buy access choir cynic D X. Or you can write it as two pi integration zero to pi access choir Synnex Dx to solve this integration consider use calls to access choir and the vehicles to cynics DX. Then by the differentiation we can say Do you use equals two two works dear. And by the integration we can say vehicles to minus cosine X. Now we can have like the formula of integration by parts which is given by integration. UDV recalls to ub minus integration VD you therefore we can right volume vehicles to 25 minus X. Esquire call sign X plus integration two weeks Cosine X DX 0 to Pi. Or we can write it as to buy minus x square cause I next plus to into integration X because the next dx zero to pi now consider use equals two X and the vehicles to called phoenix leah. Then by the differentiation we can right the US calls to DX and by the integration we can right we equals two cynics hand the volume can be written as we see the calls to 25 into minus X esquire called phoenix plus two into ex cynics minus integration sign X d x. And the limits are 0 to Pi. On fertile following we can right 25 minus X squared cause I next plus two X sign X plus two called phoenix. And the limits are 0 to Pi. So we will be called to minus two pi access Choir Cosine X plus four pi X. Synnex plus four by Cosine X. And the limits are zero to pi. Now secure the limit we get with calls to to buy By Square -4. This is the final answer for the volume. I hope you understood the solution. Thank you.


Similar Solved Questions

5 answers
COONNeaeOXCOONCooh
COON Neae OX COON Cooh...
4 answers
ProviousProb em LstNalPoint)If the serios } (x) Zor" [s & solution of tne dilterential equaticn Iy" 6then Cn+zC-Iin =1,2gonoral solutan Iho s4m10 oquation can bo wntton as }() coy () C1y2 () , whoreM(r) = 2 a1"" nW) = 2 6+7Calculate
Provious Prob em Lst Nal Point) If the serios } (x) Zor" [s & solution of tne dilterential equaticn Iy" 6 then Cn+z C-Iin =1,2 gonoral solutan Iho s4m10 oquation can bo wntton as }() coy () C1y2 () , whore M(r) = 2 a1"" nW) = 2 6+7 Calculate...
5 answers
1O8. City hotel room rates were collected for I8 U.S. cities with the data below: Hotel Room Rale by CityCuncinati 137 Columbus 044 Minm 145 Orlando 10I Tampa 139 Philudelphin Chieago 169 San Francisco 179 Dallus 155 Delroit 140 Koston 207 Atlauta 201 Los Angeles I9 Portlaud OR I65 Senttle 189 Mlinnewpolis 15; Buffalo MS Hartford CT 125 Creale the frequency distribution table for constructing histogram
1O8. City hotel room rates were collected for I8 U.S. cities with the data below: Hotel Room Rale by City Cuncinati 137 Columbus 044 Minm 145 Orlando 10I Tampa 139 Philudelphin Chieago 169 San Francisco 179 Dallus 155 Delroit 140 Koston 207 Atlauta 201 Los Angeles I9 Portlaud OR I65 Senttle 189 Mlin...
5 answers
IW More Linear Function Models and Applications: Problem 5 fti Enoam Aenian EdrcnlatMrmaMen htEenrm
IW More Linear Function Models and Applications: Problem 5 fti Enoam Aenian Edrcnlat MrmaMen htEe nrm...
5 answers
Iodine-[25 radioactive and has half Iife of 60.25 days. How much of 5.80 mg sample would be left after 40,0 days?Round your answer t0 slgnificant digits. Also, be sure your answer has unilsvmdol
Iodine-[25 radioactive and has half Iife of 60.25 days. How much of 5.80 mg sample would be left after 40,0 days? Round your answer t0 slgnificant digits. Also, be sure your answer has unilsvmdol...
5 answers
Solve the initial value problem. dy y dx =4xeX, X y(1) =4e + 1The solution is y(x) =
Solve the initial value problem. dy y dx =4xeX, X y(1) =4e + 1 The solution is y(x) =...
5 answers
Q2 _ If the lifetime X of a hearing aid battery has Weibull distribution with U = 0.1,8 = 0.5. Find the probability that such a batterywill function for more than 300 hoursb) will not last 100 hoursAlso. Findmeanvariance
Q2 _ If the lifetime X of a hearing aid battery has Weibull distribution with U = 0.1,8 = 0.5. Find the probability that such a battery will function for more than 300 hours b) will not last 100 hours Also. Find mean variance...
5 answers
Write any plausible reaction sequence of 4 steps = starting from A, B, C, or D Now; present the synthesis as retrosynthesis.
Write any plausible reaction sequence of 4 steps = starting from A, B, C, or D Now; present the synthesis as retrosynthesis....
1 answers
Solve the differential equation or initial-value problem. $$\cot y d x-x d y=0 ; y(1)=0$$
Solve the differential equation or initial-value problem. $$\cot y d x-x d y=0 ; y(1)=0$$...
5 answers
Graph the Pair of parametric equations in the rectangular coordinate system. x=t-3,y = 3t 0sts3Which of the following is the correct graph of the curve for 0 <ts3? O A.
Graph the Pair of parametric equations in the rectangular coordinate system. x=t-3,y = 3t 0sts3 Which of the following is the correct graph of the curve for 0 <ts3? O A....
5 answers
Explain why metal hydride reduction gives an endo alcohol as the major product in one reaction and an exo alcohol as the major product in the other reaction.
Explain why metal hydride reduction gives an endo alcohol as the major product in one reaction and an exo alcohol as the major product in the other reaction....
5 answers
BrandPriceScoreBose18076Skullcandy15071Koss9561Phillips7056Denon7040JVC3526Using Excel create a scatter diagram and regression output.a. Identify the regression equation.b. Using the regression output, Is there a significantrelationship using the F test. What is your conclusion? Use a =.05. Explain.c. Does the R and R-Squared clues support this? Why?
Brand Price Score Bose 180 76 Skullcandy 150 71 Koss 95 61 Phillips 70 56 Denon 70 40 JVC 35 26 Using Excel create a scatter diagram and regression output. a. Identify the regression equation. b. Using the regression output, Is there a significant relationship using the F test. What is your conclusi...
5 answers
"WJOY Isaiduis U! SUOVIJEJJ JO 543331u! se SJamsue Jnok #ND475,LA + u8s/u + pu Rv &u +y^ 'QJazuou puE aJuy S! 1531 uoSIJeduo) HJUII a4} U} ujexqo noX 3433e1 4pns 34Pinoys asooyp nokdjo anjeA J4L '33u38.34403 HWII JoebaoEeduoj apppap 0} (153} uosuueduoj HWII 84} 43iM pasn aq Pinoys sauas-d je4m apppap "sajuas BujMoljoy 341: J0 Yje3404
"WJOY Isaiduis U! SUOVIJEJJ JO 543331u! se SJamsue Jnok #ND 475, LA + u8 s/u + pu Rv &u +y^ 'QJazuou puE aJuy S! 1531 uoSIJeduo) HJUII a4} U} ujexqo noX 3433e1 4pns 34Pinoys asooyp nokdjo anjeA J4L '33u38.34403 HWII JoebaoEeduoj apppap 0} (153} uosuueduoj HWII 84} 43iM pasn aq Pin...

-- 0.022232--