5

Find the exact length of the curve given byx=2t2,y=13t3(0≤t≤1)....

Question

Find the exact length of the curve given byx=2t2,y=13t3(0≤t≤1).

Find the exact length of the curve given by x=2t2,y=13t3(0≤t≤1).



Answers

Find the exact length of the curve.

$ y = \sqrt{x - x^2} + \sin^{-1} (\sqrt{x}) $

All right, so we have a fine Exactly. Okay. And the carburettor hoses, Why is your soon next one is excess. Where place signing or so First of all the stars not defined for values off extra Vieira check. It's doing so if you talk about it. The ring of this car. So the rain will be extremist Texas. Where sure that whistles. You don't If you started beating X well, you know. Okay, we get in the middle of this one, so if I call that a demon if I call that a detail IHS moved off actually who? Minus one. And if you saw this Thanks belong so geo and starting it this actually quality. Okay, according inside. And the group should be politics for Big Green Actually, you okay? When the stakes belong for You know, if you get a position of these tools who are living, it is a demon in the section nito the sexual Bt. So they're becoming or will be zero x that is the domain of dysfunction. This dual function will be farmers. You okay now? Beautiful. I love the land of the car. Okay, So what you have to do is we have to. The future discovers Let's differentiated. So what are we legally Why This will be close to differentiation off this bus when my you Oh, don't next minus excess wet. Okay. And not the physician off disappointed. So they give one minus. Who cares? Okay, so that is the position of this and not the other difference here. Assigning less off route explored the physician off signing. Listen, this what home? One minus X s well in excess for excess entry route accion. So this angle differentiation off Route six using change. So that obesity, when my new a little X Well, everyone's different. Okay, So now if you for this isn't your fight, you see, you can get you a microphone and he can think Tex Palmer from here from severe, bigger things when I do. And home economics common. So what we have to do it is you getting off one minus two looks yet. Okay, you are way 1,000,006. Let's see any for making money for food. Ex Formula One, You go one minus Knicks. Okay. No for this. Who this on this one first, 1 30 to minus two x. So we can take to call one years of year Konia And he collected some B minus one minus Excellent man Lived off. What? My section. Yes. So you for you. What? You go for that? But my sex do I go from minus x 17? He said if I thought there really Tonto What? My sex anywhere. Any witness. Okay, so they function. No. So big question Indignation. Lonely, lonely little balls. What was it doing? What's this way? Office today You won my six. You wanted my ex before you break. So what were the indication? Zero waas. And if you think I seem to remember the X Plus One my eyes xxx begins low. So we are left it only going one upon X and then be sent You d be actually loving. He headed toward alleviating the medication off of accepting perfection in your sector. Support for excellent education off existing one minus half b This off this one. So this will be affects. They litigation off this memory for the limits. You don't know what a pretty mixed up. Remember this one? So that will be who loathe. Okay,

Hey, it's Claire. So in your radio. So we're gonna find the length of the curve for why is one minus e to negative X excess between zero and two. So the derivative we get is e to the negative X and our length Argh! Link formula from 0 to 2 square root of one plus e to the negative two x d x We're gonna substitute you square for one plus e to the negative to X So when we substitute to you, do you equals negative to e to the negative two x t x d X equals negative. You do you over you square minus one. So this changes the limits of integration and they become from negative to square root of two. Excuse me to one plus e to the negative four you times negative. You do you Over. You square minus one. We go here, this becomes equal to square it to square root of one. Pull us me to the negative for use square, do you over one minus you square which is equal to square of two square root of one plus e to the negative four you square minus one plus one over one minus you square. And this splits into two. So it splits into you. Square minus one over one minus. You square from negative too. To one plus me to the negative for do you plus read too. One plus eat the negative for do you over one minus You square We simplify this. This becomes equal to negative. You too. One. Pull us Eat the negative for do you plus route to one plus b to the negative for do you over one minus You square will continue. Here comes negative rich too. One plus e to the negative for D u plus 1/2 rich too One plus eats the negative for one minus you plus one plus you over one minus you times one plus you Do you When we simplify this this is equal to negative route too square root of one plus eat the negative for do you less 1/2 square it of two square of one plus eat the negative for becomes one over When mine issue plus one over one plus you do you And this becomes you When we ent I drive it This becomes l on negative l end of one minus you. Class Ellen of one plus you. And when we find this, this is equal to square root of two minus square root of one plus eat negative for plus 1/2 L n of one plus square root of one. Pull us eats and negative four over one minus square root of one plus Eat the negative for minus 1/2 well and one plus square of two over one minus square root of two. This is equivalent to around 2.22 one for two.

Okay, I'm gonna try to find, uh, we have You have this curve here, Michael's? Why square it was x cubed. And there are two branches. If you if you do this, why is closely minus the square root of X cubes? And we're looking interested in upper branch with a tangent to the curve. Hits the X axis at a 45 degree angle so we could see that that forms and right from angle there and we could see that that's smoke of that right triangle. The slope of the side would have to be a war. The height she moved along there. This equal, this looks equal one because changing height sequence change in the base. So we're looking for we need a point. The cornice of that point X coordinates and we could find our client's home here. So what you do is you because the slope is one you can take into repetitive. Why prime? I'm gonna work with this guy here. The positive version of this, which is going to give me a well, much looking this way, is just one for minus X 23. So are driven me three halves. Actually, 1/2. I'm gonna change the black hair. Is this so why prime is three hands. Excellent warning. We're gonna have to square that that would become a nine. Ford's X. It's gonna go into art. But in any case, when does this equal more? Because that's you will repair that. We're interested in the X. So that's including one when accident one equals 2/3. So x is four nights square both sides. So that's our king. Number are our clients will be from 049 square root of one plus 94 sex T X. The only thing we need in great this is and factor nine force. We need that. That's if this is to be thought of you to the end. Eu Then we could see that are you is the nine for its X. So do you must be forts, the X So we just need the nine for. So put that in nine starts for the four nights out here and you have what you know amount, switch back. Switch over to my rational form here. Okay, So I have that and that becomes four nines and we'll have one plus nine Fords to the three halves times a 2/3 from 0 to 4. Giants. Wish becomes eagle 27 time since there's accent. I'm sorry about that, Uh, one last night. So have a one plus nine Fords, times or nines. Three hands minus one 0 to 3 halves that becomes a plant becomes See you here, H 1/7. And inside here is that we hits them to to the three hands and then minus one. Okay, uh, can do much more with that, But we can write two to minus one certainly. And it would be good enough.

Hey, it's Claire. So when you right here. So we have. Why is equal to one plus six x to the three hounds. When we differentiate this, we get d Y over D. X is equal to nine x to the one, huh? And using the art length formula we get l is equal to from 0 to 1 square e one plus nine x the 1/2 square d x this is equal to from 0 to 1 square root of one plus 81 x e x. We're gonna let you be equal to one plus 81 x So do you is equal to 81 d x. So this gives us well is equal to one over 81. And here we're gonna change the limits of integration. So a is equal to 82 and B is equal to one. So we put one 82 square root of you and then this gives us to over 243 Time 82 spirit of 82 minus one


Similar Solved Questions

5 answers
A-How many different six letter arrangements of the letters in the word google are there?
a-How many different six letter arrangements of the letters in the word google are there?...
3 answers
Lathe untversathe si of all real numb4S,, ard let A {eRI-s* 0}, 0 ={xeR-1<* < 2}, amd €={xeR/5<*<7}exh of die fullawrig:AU L {reel-3sx<2} {ree|- e*s2} {reklxs- 7Or * > {e#kx<-Jorx22}AnB {rew| 5}< {rem/-1exsv} {remkx <-1 On { ? {xerk < Or> >{rem/-3 <x <o} {xcw/-3sxso} {reklxs- 73Or * 2 {xeekx < 3or* >Auc {reB| sfsm5 <xs7; {Ke#| Uc , <xsti {Ke#| sfsm5 <x<71 {re#| 9*<0 and 5 <*s7f
Lathe untversa the si of all real numb4S,, ard let A {eRI-s* 0}, 0 ={xeR-1<* < 2}, amd €={xeR/5<*<7} exh of die fullawrig: AU L {reel-3sx<2} {ree|- e*s2} {reklxs- 7Or * > {e#kx<-Jorx22} AnB {rew| 5}< {rem/-1exsv} {remkx <-1 On { ? {xerk < Or> > {rem/-3 <x...
5 answers
Mainixmsan aigenvu lue A -2 0f muiiolicitv J with One independent #idenvector_The solurion of the WR X-4X Xo)--HJat [22 I
Mainix msan aigenvu lue A -2 0f muiiolicitv J with One independent #idenvector_ The solurion of the WR X-4X Xo)- -HJ at [22 I...
5 answers
Point) Let2 | and 02 3| Let T : R? ~ R? be the Iinear transformation satisfying 24 T(u and T(uz) -25Find the image of an arbitrary vector([;])
point) Let 2 | and 02 3| Let T : R? ~ R? be the Iinear transformation satisfying 24 T(u and T(uz) -25 Find the image of an arbitrary vector ([;])...
5 answers
Find the slant asymptote ol the graph = ol the rational function: use Ihe slant asympiote graph the ralianal function: Follow the seven-step strategy and |I(x)
Find the slant asymptote ol the graph = ol the rational function: use Ihe slant asympiote graph the ralianal function: Follow the seven-step strategy and | I(x)...
5 answers
T 0 lim COS 0-+0 sin 03_
T 0 lim COS 0-+0 sin 0 3_...
5 answers
(30 pts) Let the funetion f (1) ~4 622 + 91 be given.a) Determine the €-intercepts and y-intercepts of the graph of the function f. b) Find the intervals On which f is increasing and decreasing: Identify the funetion s local extreme values, if any; stating where they are taken OH _d) Find the intervals on which f is concave Up and concave down, Determine the inflection points, if any.E) Sketch the general shape of f
(30 pts) Let the funetion f (1) ~4 622 + 91 be given. a) Determine the €-intercepts and y-intercepts of the graph of the function f. b) Find the intervals On which f is increasing and decreasing: Identify the funetion s local extreme values, if any; stating where they are taken OH _ d) Find th...
5 answers
Question 3 (1 point)What consensus sequence is found on -10 nucleotides upstream of the transcription initiation site in E coli?TATATATTTTTATATTTTTATAATQuestion 4 (1 point) What gene expresses the enzyme B-galactosidase in lac operon of E col?IacAlacZlacYlacBQuestion 5 (1 point)What is the intracellular inducer for the lac operons in E coli?AlloglucoseLactoseAllolactoseGlucose
Question 3 (1 point) What consensus sequence is found on -10 nucleotides upstream of the transcription initiation site in E coli? TATATA TTTTTA TATTTT TATAAT Question 4 (1 point) What gene expresses the enzyme B-galactosidase in lac operon of E col? IacA lacZ lacY lacB Question 5 (1 point) What is t...
4 answers
OnCs_(10 points) The half-life of plutonium-241 is 13 years. How much of an initial 2-gram sample remains after 5 years? Round your answer to three decimal places
onCs_ (10 points) The half-life of plutonium-241 is 13 years. How much of an initial 2-gram sample remains after 5 years? Round your answer to three decimal places...
5 answers
How many of the following are substantially soluble inhexane?KBrCaBr 2I 2LiBrC 6H 6
How many of the following are substantially soluble in hexane? KBr CaBr 2 I 2 LiBr C 6H 6...
5 answers
Aratoll Hab ?MT natanae04 UUU IIrpint X IlieAuln Ino nrotel IureAruili nantuscicy Ir-himute I4ntrojgn +o TIlte otdth IFte LtuLoicnue
Aratoll Hab ? MT natanae 04 UUU I Irpint X Ilie Auln Ino nrotel IureAruili nantu scicy Ir-himute I4ntrojgn +o TIlte otdth IFte LtuL oicnue...
5 answers
Amy performed a box cox analysis in jmp. she found a lambda equal to -.01, what would be the recommended re-expression of y?1. take the log of the y values2. take the square of the y values 3. you don't need to re-express the data
Amy performed a box cox analysis in jmp. she found a lambda equal to -.01, what would be the recommended re-expression of y? 1. take the log of the y values 2. take the square of the y values 3. you don't need to re-express the data...
5 answers
Q1a.When the Ag+ concentrationis 5.54×10-4 M, the observedcell potential at 298K for an electrochemical cell with thefollowing reaction is 1.345V. What isthe Cr3+ concentration?3Ag+(aq) + Cr(s)3Ag(s) + Cr3+(aq)Answer: -------MQ1b.When the Ag+ concentrationis 8.15×10-4 M, the observedcell potential at 298K for an electrochemical cell with thefollowing reaction is 1.375V. What isthe Zn2+ concentration?2Ag+(aq) + Zn(s)2Ag(s) + Zn2+(aq)Answer:------- M
Q1a. When the Ag+ concentration is 5.54×10-4 M, the observed cell potential at 298K for an electrochemical cell with the following reaction is 1.345V. What is the Cr3+ concentration? 3Ag+(aq) + Cr(s)3Ag(s) + Cr3+(aq) Answer: -------M Q1b. When the Ag+ concentration is 8.15×10-4 M, the obser...
5 answers
The following figures show several molecular georetries . For each geometry, give the electron domain genmetry of the central atom; Ihe number bond5, and Ine number of Ione pairs around Ihe cenral alom; points each; points (otal)
The following figures show several molecular georetries . For each geometry, give the electron domain genmetry of the central atom; Ihe number bond5, and Ine number of Ione pairs around Ihe cenral alom; points each; points (otal)...
5 answers
Revic ConstantsPart AComplete the following reaction,[I;, 1LODraw the molecule on the canvas by choosing buttons from the Tools (for bonds} Atoms Advanced Template toolbars The single bond is active by defaul:Ht p2 0 0 /0
Revic Constants Part A Complete the following reaction, [I;, 1LO Draw the molecule on the canvas by choosing buttons from the Tools (for bonds} Atoms Advanced Template toolbars The single bond is active by defaul: Ht p2 0 0 / 0...
5 answers
What does “Carbon Copy” (the first cloned cat) look like? a.Black and white b. Orange and white c. Calico (white, orange, andblack) d. All black e. All orange
What does “Carbon Copy” (the first cloned cat) look like? a. Black and white b. Orange and white c. Calico (white, orange, and black) d. All black e. All orange...
5 answers
Orbitals_ 4is a lone pair in a orbital: Xis hybridized, Y is hybridized, and Z is hybridized; There are hydrogens in this molecule Based on the bonding pattern here; the element identity for X; Y,and Z could be:3D4
orbitals_ 4is a lone pair in a orbital: Xis hybridized, Y is hybridized, and Z is hybridized; There are hydrogens in this molecule Based on the bonding pattern here; the element identity for X; Y,and Z could be: 3 D 4...
5 answers
(5 points) Civen 2 % since 0 0 i4 root of ," e Gls]: the Factor Thcorcm tclk u that (I - I) dlivides 1. " A(=) € Qkl tthe quotient . then:fa(r)+0+1Show that I,(r) i ureducibl &er Q if and ouly ff n 1 prime. (Hint: If n p In pEIe and % =I -1 then J(r) = Ilu + 4) (( + Iy T)u: Simplily ad us Eisenstein - Criteriou )
(5 points) Civen 2 % since 0 0 i4 root of ," e Gls]: the Factor Thcorcm tclk u that (I - I) dlivides 1. " A(=) € Qkl tthe quotient . then: fa(r) +0+1 Show that I,(r) i ureducibl &er Q if and ouly ff n 1 prime. (Hint: If n p In pEIe and % =I -1 then J(r) = Ilu + 4) (( + Iy T)u: Si...
5 answers
Mlovng another question Wll save this responsa.QuestionQuestion1,8 PelnsUn form magnetic fel pcints out 0f the page shown; Tnree parucies shot Into the region KucA shown: Indicate the sign of charges on the particles _and respectively:Oa I _ Cbis - Qa is. Qb is' + , Qc Qc Is.Jnctne queston Kaill save tnis response_Question
Mlovng another question Wll save this responsa. Question Question 1,8 Pelns Un form magnetic fel pcints out 0f the page shown; Tnree parucies shot Into the region KucA shown: Indicate the sign of charges on the particles _ and respectively: Oa I _ Cbis - Qa is. Qb is' + , Qc Qc Is. Jnctne quest...
5 answers
Subtract IXiKXiX-X-12 x Sx +47 *12 X -5x+4(Simplify your answer: )
Subtract IXi KXi X-X-12 x Sx +4 7 *12 X -5x+4 (Simplify your answer: )...

-- 0.019675--