calculus parametric curve length The Next CEO of Stack OverflowFind the length of the...

If the heap is initialized for security, then why is the stack uninitialized?

How to solve a differential equation with a term to a power?

How did people program for Consoles with multiple CPUs?

Sending manuscript to multiple publishers

Different harmonic changes implied by a simple descending scale

Example of a Mathematician/Physicist whose Other Publications during their PhD eclipsed their PhD Thesis

Can we say or write : "No, it'sn't"?

Is HostGator storing my password in plaintext?

Is it ever safe to open a suspicious html file (e.g. email attachment)?

Why do we use the plural of movies in this phrase "We went to the movies last night."?

Why am I allowed to create multiple unique pointers from a single object?

What happened in Rome, when the western empire "fell"?

Why did we only see the N-1 starfighters in one film?

Why do professional authors make "consistency" mistakes? And how to avoid them?

Can I equip Skullclamp on a creature I am sacrificing?

What is the purpose of the Evocation wizard's Potent Cantrip feature?

Limits on contract work without pre-agreed price/contract (UK)

What flight has the highest ratio of time difference to flight time?

Anatomically Correct Strange Women In Ponds Distributing Swords

How did the Bene Gesserit know how to make a Kwisatz Haderach?

Complex fractions

Elegant way to replace substring in a regex with optional groups in Python?

What connection does MS Office have to Netscape Navigator?

Can you replace a racial trait cantrip when leveling up?



calculus parametric curve length



The Next CEO of Stack OverflowFind the length of the parametric curve (Difficult)Parametric Curve Tangent EquationsParametric curve parametriced by lengthCompute the length of a parametric curve.Arc Length parametric curveSampling a curve (parametric)Arc Length with Parametric EquationsFind the length of the parametric curveTransforming quadratic parametric curve to implicit formLength of a parametric curve formula: What does the integral represent?












3












$begingroup$


Find the length of the following parametric curve.



$x  =  5  +  frac92 t^3$ , $y  =  4  +  3 t^{frac92}$ , $0 leq  t leq  2$.



I used integration and after some point I got lost :( Can anyone show me the steps?






calculus parametric







share|cite|improve this question











$endgroup$












  • $begingroup$
    Is this $$x=5+frac{9}{2}t^3,y=4+3t^{9/2}$$?
    $endgroup$
    – Dr. Sonnhard Graubner
    4 hours ago


















3












$begingroup$


Find the length of the following parametric curve.



$x  =  5  +  frac92 t^3$ , $y  =  4  +  3 t^{frac92}$ , $0 leq  t leq  2$.



I used integration and after some point I got lost :( Can anyone show me the steps?






calculus parametric







share|cite|improve this question











$endgroup$












  • $begingroup$
    Is this $$x=5+frac{9}{2}t^3,y=4+3t^{9/2}$$?
    $endgroup$
    – Dr. Sonnhard Graubner
    4 hours ago
















3












3








3





$begingroup$


Find the length of the following parametric curve.



$x  =  5  +  frac92 t^3$ , $y  =  4  +  3 t^{frac92}$ , $0 leq  t leq  2$.



I used integration and after some point I got lost :( Can anyone show me the steps?






calculus parametric







share|cite|improve this question











$endgroup$




Find the length of the following parametric curve.



$x  =  5  +  frac92 t^3$ , $y  =  4  +  3 t^{frac92}$ , $0 leq  t leq  2$.



I used integration and after some point I got lost :( Can anyone show me the steps?






calculus parametric




calculus parametric






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 4 hours ago









Matt A Pelto

2,667621




2,667621










asked 4 hours ago









McAMcA

224




224












  • $begingroup$
    Is this $$x=5+frac{9}{2}t^3,y=4+3t^{9/2}$$?
    $endgroup$
    – Dr. Sonnhard Graubner
    4 hours ago




















  • $begingroup$
    Is this $$x=5+frac{9}{2}t^3,y=4+3t^{9/2}$$?
    $endgroup$
    – Dr. Sonnhard Graubner
    4 hours ago


















$begingroup$
Is this $$x=5+frac{9}{2}t^3,y=4+3t^{9/2}$$?
$endgroup$
– Dr. Sonnhard Graubner
4 hours ago






$begingroup$
Is this $$x=5+frac{9}{2}t^3,y=4+3t^{9/2}$$?
$endgroup$
– Dr. Sonnhard Graubner
4 hours ago












3 Answers
3






active

oldest

votes


















2












$begingroup$

Apply the formula for arc length, we get
$$
int_0^2 frac{27{{t}^{2}},sqrt{{{t}^{3}}+1}}{2} dt
$$
Then we make the change of variable $v=t^3+1$ to get
$$
int_1^9 frac 9 2 sqrt{v} dv = 78.
$$






share|cite|improve this answer








New contributor




EagleToLearn is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






$endgroup$





















    2












    $begingroup$

    begin{aligned}L&=int_0^2 sqrt{frac{729}4t^4+frac{729}4t^7}dt\&=int_0^2sqrt{frac{729}4t^4(1+t^3)}dt\&=frac{27}2int_0^2t^2(1+t^3)^{frac12}dt\&=3(1+t^3)^{frac32}big]_0^2end{aligned}



    Made the leap from the third line to the fourth line by recognizing that $F(t)=3(1+t^3)^{frac32}$ is an antiderivative of $f(t)=frac{27}2t^2(1+t^3)^{frac12}$.






    share|cite|improve this answer











    $endgroup$





















      1












      $begingroup$

      You must use the formula $$int_{0}^{2}sqrt{left(frac{dx}{dt}right)^2+left(frac{dy}{dt}right)^2}dt$$
      $$dx=frac{9}{2}3t^2dt$$ and $$dy=3cdot frac{9}{2}t^{7/2}dt$$






      share|cite|improve this answer









      $endgroup$














        Your Answer





        StackExchange.ifUsing("editor", function () {
        return StackExchange.using("mathjaxEditing", function () {
        StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
        StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
        });
        });
        }, "mathjax-editing");

        StackExchange.ready(function() {
        var channelOptions = {
        tags: "".split(" "),
        id: "69"
        };
        initTagRenderer("".split(" "), "".split(" "), channelOptions);

        StackExchange.using("externalEditor", function() {
        // Have to fire editor after snippets, if snippets enabled
        if (StackExchange.settings.snippets.snippetsEnabled) {
        StackExchange.using("snippets", function() {
        createEditor();
        });
        }
        else {
        createEditor();
        }
        });

        function createEditor() {
        StackExchange.prepareEditor({
        heartbeatType: 'answer',
        autoActivateHeartbeat: false,
        convertImagesToLinks: true,
        noModals: true,
        showLowRepImageUploadWarning: true,
        reputationToPostImages: 10,
        bindNavPrevention: true,
        postfix: "",
        imageUploader: {
        brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
        contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
        allowUrls: true
        },
        noCode: true, onDemand: true,
        discardSelector: ".discard-answer"
        ,immediatelyShowMarkdownHelp:true
        });


        }
        });














        draft saved

        draft discarded


















        StackExchange.ready(
        function () {
        StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3167507%2fcalculus-parametric-curve-length%23new-answer', 'question_page');
        }
        );

        Post as a guest















        Required, but never shown

























        3 Answers
        3






        active

        oldest

        votes








        3 Answers
        3






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes









        2












        $begingroup$

        Apply the formula for arc length, we get
        $$
        int_0^2 frac{27{{t}^{2}},sqrt{{{t}^{3}}+1}}{2} dt
        $$
        Then we make the change of variable $v=t^3+1$ to get
        $$
        int_1^9 frac 9 2 sqrt{v} dv = 78.
        $$






        share|cite|improve this answer








        New contributor




        EagleToLearn is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
        Check out our Code of Conduct.






        $endgroup$


















          2












          $begingroup$

          Apply the formula for arc length, we get
          $$
          int_0^2 frac{27{{t}^{2}},sqrt{{{t}^{3}}+1}}{2} dt
          $$
          Then we make the change of variable $v=t^3+1$ to get
          $$
          int_1^9 frac 9 2 sqrt{v} dv = 78.
          $$






          share|cite|improve this answer








          New contributor




          EagleToLearn is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.






          $endgroup$
















            2












            2








            2





            $begingroup$

            Apply the formula for arc length, we get
            $$
            int_0^2 frac{27{{t}^{2}},sqrt{{{t}^{3}}+1}}{2} dt
            $$
            Then we make the change of variable $v=t^3+1$ to get
            $$
            int_1^9 frac 9 2 sqrt{v} dv = 78.
            $$






            share|cite|improve this answer








            New contributor




            EagleToLearn is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.






            $endgroup$



            Apply the formula for arc length, we get
            $$
            int_0^2 frac{27{{t}^{2}},sqrt{{{t}^{3}}+1}}{2} dt
            $$
            Then we make the change of variable $v=t^3+1$ to get
            $$
            int_1^9 frac 9 2 sqrt{v} dv = 78.
            $$







            share|cite|improve this answer








            New contributor




            EagleToLearn is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.









            share|cite|improve this answer



            share|cite|improve this answer






            New contributor




            EagleToLearn is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.









            answered 4 hours ago









            EagleToLearnEagleToLearn

            233




            233




            New contributor




            EagleToLearn is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.





            New contributor





            EagleToLearn is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.






            EagleToLearn is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
            Check out our Code of Conduct.























                2












                $begingroup$

                begin{aligned}L&=int_0^2 sqrt{frac{729}4t^4+frac{729}4t^7}dt\&=int_0^2sqrt{frac{729}4t^4(1+t^3)}dt\&=frac{27}2int_0^2t^2(1+t^3)^{frac12}dt\&=3(1+t^3)^{frac32}big]_0^2end{aligned}



                Made the leap from the third line to the fourth line by recognizing that $F(t)=3(1+t^3)^{frac32}$ is an antiderivative of $f(t)=frac{27}2t^2(1+t^3)^{frac12}$.






                share|cite|improve this answer











                $endgroup$


















                  2












                  $begingroup$

                  begin{aligned}L&=int_0^2 sqrt{frac{729}4t^4+frac{729}4t^7}dt\&=int_0^2sqrt{frac{729}4t^4(1+t^3)}dt\&=frac{27}2int_0^2t^2(1+t^3)^{frac12}dt\&=3(1+t^3)^{frac32}big]_0^2end{aligned}



                  Made the leap from the third line to the fourth line by recognizing that $F(t)=3(1+t^3)^{frac32}$ is an antiderivative of $f(t)=frac{27}2t^2(1+t^3)^{frac12}$.






                  share|cite|improve this answer











                  $endgroup$
















                    2












                    2








                    2





                    $begingroup$

                    begin{aligned}L&=int_0^2 sqrt{frac{729}4t^4+frac{729}4t^7}dt\&=int_0^2sqrt{frac{729}4t^4(1+t^3)}dt\&=frac{27}2int_0^2t^2(1+t^3)^{frac12}dt\&=3(1+t^3)^{frac32}big]_0^2end{aligned}



                    Made the leap from the third line to the fourth line by recognizing that $F(t)=3(1+t^3)^{frac32}$ is an antiderivative of $f(t)=frac{27}2t^2(1+t^3)^{frac12}$.






                    share|cite|improve this answer











                    $endgroup$



                    begin{aligned}L&=int_0^2 sqrt{frac{729}4t^4+frac{729}4t^7}dt\&=int_0^2sqrt{frac{729}4t^4(1+t^3)}dt\&=frac{27}2int_0^2t^2(1+t^3)^{frac12}dt\&=3(1+t^3)^{frac32}big]_0^2end{aligned}



                    Made the leap from the third line to the fourth line by recognizing that $F(t)=3(1+t^3)^{frac32}$ is an antiderivative of $f(t)=frac{27}2t^2(1+t^3)^{frac12}$.







                    share|cite|improve this answer














                    share|cite|improve this answer



                    share|cite|improve this answer








                    edited 3 hours ago

























                    answered 4 hours ago









                    Matt A PeltoMatt A Pelto

                    2,667621




                    2,667621























                        1












                        $begingroup$

                        You must use the formula $$int_{0}^{2}sqrt{left(frac{dx}{dt}right)^2+left(frac{dy}{dt}right)^2}dt$$
                        $$dx=frac{9}{2}3t^2dt$$ and $$dy=3cdot frac{9}{2}t^{7/2}dt$$






                        share|cite|improve this answer









                        $endgroup$


















                          1












                          $begingroup$

                          You must use the formula $$int_{0}^{2}sqrt{left(frac{dx}{dt}right)^2+left(frac{dy}{dt}right)^2}dt$$
                          $$dx=frac{9}{2}3t^2dt$$ and $$dy=3cdot frac{9}{2}t^{7/2}dt$$






                          share|cite|improve this answer









                          $endgroup$
















                            1












                            1








                            1





                            $begingroup$

                            You must use the formula $$int_{0}^{2}sqrt{left(frac{dx}{dt}right)^2+left(frac{dy}{dt}right)^2}dt$$
                            $$dx=frac{9}{2}3t^2dt$$ and $$dy=3cdot frac{9}{2}t^{7/2}dt$$






                            share|cite|improve this answer









                            $endgroup$



                            You must use the formula $$int_{0}^{2}sqrt{left(frac{dx}{dt}right)^2+left(frac{dy}{dt}right)^2}dt$$
                            $$dx=frac{9}{2}3t^2dt$$ and $$dy=3cdot frac{9}{2}t^{7/2}dt$$







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered 4 hours ago









                            Dr. Sonnhard GraubnerDr. Sonnhard Graubner

                            78.2k42867




                            78.2k42867






























                                draft saved

                                draft discarded




















































                                Thanks for contributing an answer to Mathematics Stack Exchange!


                                • Please be sure to answer the question. Provide details and share your research!

                                But avoid …



                                • Asking for help, clarification, or responding to other answers.

                                • Making statements based on opinion; back them up with references or personal experience.


                                Use MathJax to format equations. MathJax reference.


                                To learn more, see our tips on writing great answers.




                                draft saved


                                draft discarded














                                StackExchange.ready(
                                function () {
                                StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3167507%2fcalculus-parametric-curve-length%23new-answer', 'question_page');
                                }
                                );

                                Post as a guest















                                Required, but never shown





















































                                Required, but never shown














                                Required, but never shown












                                Required, but never shown







                                Required, but never shown

































                                Required, but never shown














                                Required, but never shown












                                Required, but never shown







                                Required, but never shown







                                -

                                Popular posts from this blog

                                Щит и меч (фильм) Содержание Названия серий | Сюжет |...

                                Image
                                Фильмы по алфавитуФильмы 1968 годаФильмы СССР 1968 годаЧёрно-белые фильмы СССРФильмы студии «Мосфильм»Лидеры советского кинопрокатаФильмы-драмы СССРФильмы о Второй мировой войнеФильмы о шпионахЭкранизации произведений Вадима КожевниковаФильмы Владимира БасоваФильмы о фашизме 1968 годуодноимённому романуВадима КожевниковаВладимиром БасовымСтанислав ЛюбшинГерманиюАбверегауптштурмфюрераССБерлинслужбу СДSchwarzbraun ist die HaselnussXVIII векаЭрикиХермса НиляГитлерюгендаАбвераАх, мой милый АвгустинXVII векаHorst WesselDeutschland über alles У этого термина существуют и другие значения, см. Щит и меч. Щит и меч Жанр драма военный фильм Режиссёр Владимир Басов Автор сценария Владимир Басов Вадим Кожевников В главных ролях Станислав Любшин Валентина Титова Олег Янковский Георгий Мартынюк Владимир Басов Оператор Тимофей Лебешев Композитор Вениамин Баснер Кинокомпания Киностудия «Мосфильм». Творческое объединение писателей и киноработников ...
                                Read more

                                Венесуэла на летних Олимпийских играх 2000 Содержание Состав...

                                Image
                                БангладешБахрейнБутанБрунейВьетнамГонконгИндияИндонезияИорданияИракИранЙеменКазахстанКамбоджаКатарКитайКиргизияКНДРКувейтЛаосЛиванМалайзияМальдивыМонголияМьянмаНепалОАЭОман ПакистанГосударство ПалестинаСаудовская АравияСингапурСирияТаджикистанТаиландТайваньТуркменияУзбекистанФилиппиныШри-ЛанкаЮжная КореяЯпонияИндивидуальные олимпийские спортсменыАлжирАнголаБенинБотсванаБуркина-ФасоБурундиГабонГамбияГанаГвинеяГвинея-БисауДемократическая Республика КонгоДжибутиЕгипетЗамбияЗимбабвеКабо-ВердеКамерунКенияКоморские островаКот-д’ИвуарЛесотоЛиберияЛивияМаврикийМавританияМадагаскарМалавиМалиМароккоМозамбикНамибияНигерНигерияРеспублика КонгоРуандаСан-Томе и ПринсипиСвазилендСейшелыСенегалСомалиСуданСьерра-ЛеонеТанзанияТогоТунисУгандаЦентральноафриканская РеспубликаЧадЭкваториальная ГвинеяЭритреяЭфиопияЮАРАвстралияАмериканское СамоаВануатуГуамМикронезияНауруНовая ЗеландияОстрова КукаПалауПапуа — Новая ГвинеяСамоаСоломоновы ОстроваТонгаФиджи Венесуэла на Олимпийских играх2000 год в ВенесуэлеСтран...
                                Read more

                                Meter-Bus Содержание Параметры шины | Стандартизация |...

                                Image
                                RS-232IrDAHARTмодемтоковая петляИРПСMIDIIO-LinkRS-422RS-423RS-485LINM-BusKansas City StandardКомпакт-кассетагрампластинкаPPPSLIPIrDAHARTISO 7816MIDIIO-LinkModbusLINDMX-512P-NETProfibusIEC 608708250 UART16550 UART Сетевые протоколыПоследовательные шины физического уровняполевой шиныасинхронного интерфейсаOpen Metering SystemAESздесь У этого термина существуют и другие значения, см. M-bus (значения). M-Bus (Meter-Bus) — стандарт физического уровня для полевой шины на основе асинхронного интерфейса. Также под этим названием понимают коммуникационный протокол, используемый для связи устройств по этой шине. M-bus преимущественно применяется для приборов учета электрической энергии (электросчётчики), тепловой энергии (теплосчётчики), расходомеров воды и газа. Данные передаются на компьютерную станцию (сервер) напрямую или через концентраторы шины M-Bus, а также усилители-повторители сигнала. Содержание 1 Параметры шины 2 Стандартизация 2.1 Open Metering System ...
                                Read more