Parametric curve length - calculus The Next CEO of Stack OverflowDetect “cusp” in parametric curveFind the length of the parametric curve (Difficult)Parametric 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 curveDetermine the length of the Parametric Curve given by the set of parametric equations.Length of a parametric curve formula: What does the integral represent?

Multi tool use
Multi tool use

Rotate a column

If a black hole is created from light, can this black hole then move at speed of light?

How to avoid supervisors with prejudiced views?

Anatomically Correct Strange Women In Ponds Distributing Swords

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

I believe this to be a fraud - hired, then asked to cash check and send cash as Bitcoin

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

How fast would a person need to move to trick the eye?

Why do airplanes bank sharply to the right after air-to-air refueling?

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

Why has the US not been more assertive in confronting Russia in recent years?

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

Won the lottery - how do I keep the money?

Is there a difference between "Fahrstuhl" and "Aufzug"

How to count occurrences of text in a file?

What does convergence in distribution "in the Gromov–Hausdorff" sense mean?

How do scammers retract money, while you can’t?

Is "for causing autism in X" grammatical?

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

Is HostGator storing my password in plaintext?

Novel about a guy who is possessed by the divine essence and the world ends?

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

Is there an analogue of projective spaces for proper schemes?

MessageLevel in QGIS3



Parametric curve length - calculus



The Next CEO of Stack OverflowDetect “cusp” in parametric curveFind the length of the parametric curve (Difficult)Parametric 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 curveDetermine the length of the Parametric Curve given by the set of parametric equations.Length 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 :( What are the steps?






calculus parametric







share|cite|improve this question











$endgroup$











  • $begingroup$
    Is this $$x=5+frac92t^3,y=4+3t^9/2$$?
    $endgroup$
    – Dr. Sonnhard Graubner
    5 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 :( What are the steps?






calculus parametric







share|cite|improve this question











$endgroup$











  • $begingroup$
    Is this $$x=5+frac92t^3,y=4+3t^9/2$$?
    $endgroup$
    – Dr. Sonnhard Graubner
    5 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 :( What are 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 :( What are 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 6 mins ago









Peter Mortensen

565310




565310










asked 6 hours ago









McAMcA

204




204











  • $begingroup$
    Is this $$x=5+frac92t^3,y=4+3t^9/2$$?
    $endgroup$
    – Dr. Sonnhard Graubner
    5 hours ago

















  • $begingroup$
    Is this $$x=5+frac92t^3,y=4+3t^9/2$$?
    $endgroup$
    – Dr. Sonnhard Graubner
    5 hours ago
















$begingroup$
Is this $$x=5+frac92t^3,y=4+3t^9/2$$?
$endgroup$
– Dr. Sonnhard Graubner
5 hours ago





$begingroup$
Is this $$x=5+frac92t^3,y=4+3t^9/2$$?
$endgroup$
– Dr. Sonnhard Graubner
5 hours ago











3 Answers
3






active

oldest

votes


















2












$begingroup$

Apply the formula for arc length, we get
$$
int_0^2 frac27t^2,sqrtt^3+12 dt
$$
Then we make the change of variable $v=t^3+1$ to get
$$
int_1^9 frac 9 2 sqrtv dv = 78.
$$






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












    $begingroup$

    beginalignedL&=int_0^2 sqrtfrac7294t^4+frac7294t^7dt\&=int_0^2sqrtfrac7294t^4(1+t^3)dt\&=frac272int_0^2t^2(1+t^3)^frac12dt\&=3(1+t^3)^frac32big]_0^2endaligned



    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 $f(t)=frac272t^2(1+t^3)^frac12$.






    share|cite|improve this answer











    $endgroup$




















      1












      $begingroup$

      You must use the formula $$int_0^2sqrtleft(fracdxdtright)^2+left(fracdydtright)^2dt$$
      $$dx=frac923t^2dt$$ and $$dy=3cdot frac92t^7/2dt$$






      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%2fparametric-curve-length-calculus%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
        $$
        int_0^2 frac27t^2,sqrtt^3+12 dt
        $$
        Then we make the change of variable $v=t^3+1$ to get
        $$
        int_1^9 frac 9 2 sqrtv dv = 78.
        $$






        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
          $$
          int_0^2 frac27t^2,sqrtt^3+12 dt
          $$
          Then we make the change of variable $v=t^3+1$ to get
          $$
          int_1^9 frac 9 2 sqrtv dv = 78.
          $$






          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
            $$
            int_0^2 frac27t^2,sqrtt^3+12 dt
            $$
            Then we make the change of variable $v=t^3+1$ to get
            $$
            int_1^9 frac 9 2 sqrtv dv = 78.
            $$






            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
            $$
            int_0^2 frac27t^2,sqrtt^3+12 dt
            $$
            Then we make the change of variable $v=t^3+1$ to get
            $$
            int_1^9 frac 9 2 sqrtv dv = 78.
            $$







            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 5 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












                $begingroup$

                beginalignedL&=int_0^2 sqrtfrac7294t^4+frac7294t^7dt\&=int_0^2sqrtfrac7294t^4(1+t^3)dt\&=frac272int_0^2t^2(1+t^3)^frac12dt\&=3(1+t^3)^frac32big]_0^2endaligned



                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 $f(t)=frac272t^2(1+t^3)^frac12$.






                share|cite|improve this answer











                $endgroup$

















                  2












                  $begingroup$

                  beginalignedL&=int_0^2 sqrtfrac7294t^4+frac7294t^7dt\&=int_0^2sqrtfrac7294t^4(1+t^3)dt\&=frac272int_0^2t^2(1+t^3)^frac12dt\&=3(1+t^3)^frac32big]_0^2endaligned



                  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 $f(t)=frac272t^2(1+t^3)^frac12$.






                  share|cite|improve this answer











                  $endgroup$















                    2












                    2








                    2





                    $begingroup$

                    beginalignedL&=int_0^2 sqrtfrac7294t^4+frac7294t^7dt\&=int_0^2sqrtfrac7294t^4(1+t^3)dt\&=frac272int_0^2t^2(1+t^3)^frac12dt\&=3(1+t^3)^frac32big]_0^2endaligned



                    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 $f(t)=frac272t^2(1+t^3)^frac12$.






                    share|cite|improve this answer











                    $endgroup$



                    beginalignedL&=int_0^2 sqrtfrac7294t^4+frac7294t^7dt\&=int_0^2sqrtfrac7294t^4(1+t^3)dt\&=frac272int_0^2t^2(1+t^3)^frac12dt\&=3(1+t^3)^frac32big]_0^2endaligned



                    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 $f(t)=frac272t^2(1+t^3)^frac12$.







                    share|cite|improve this answer














                    share|cite|improve this answer



                    share|cite|improve this answer








                    edited 5 hours ago

























                    answered 5 hours ago









                    Matt A PeltoMatt A Pelto

                    2,667621




                    2,667621





















                        1












                        $begingroup$

                        You must use the formula $$int_0^2sqrtleft(fracdxdtright)^2+left(fracdydtright)^2dt$$
                        $$dx=frac923t^2dt$$ and $$dy=3cdot frac92t^7/2dt$$






                        share|cite|improve this answer









                        $endgroup$

















                          1












                          $begingroup$

                          You must use the formula $$int_0^2sqrtleft(fracdxdtright)^2+left(fracdydtright)^2dt$$
                          $$dx=frac923t^2dt$$ and $$dy=3cdot frac92t^7/2dt$$






                          share|cite|improve this answer









                          $endgroup$















                            1












                            1








                            1





                            $begingroup$

                            You must use the formula $$int_0^2sqrtleft(fracdxdtright)^2+left(fracdydtright)^2dt$$
                            $$dx=frac923t^2dt$$ and $$dy=3cdot frac92t^7/2dt$$






                            share|cite|improve this answer









                            $endgroup$



                            You must use the formula $$int_0^2sqrtleft(fracdxdtright)^2+left(fracdydtright)^2dt$$
                            $$dx=frac923t^2dt$$ and $$dy=3cdot frac92t^7/2dt$$







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered 5 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%2fparametric-curve-length-calculus%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







                                lm e1XJ8tzDzLZIYUC,4Kw4fZx,V2,3nH2wNM JwvymzKz6KUxL5zqwD0Qe51vBOwupQiI,78D,Vr,f,zWbKLDXrSSdyL
                                -
                                EyEEEC0Qxh H

                                Popular posts from this blog

                                Creating centerline of river in QGIS? The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Finding centrelines from polygons in QGIS?Splitting line into two lines with GRASS GIS?Centroid of the equator and a pointpostgis: problems creating flow direction polyline; not all needed connections are drawnhow to make decent sense from scattered river depth measurementsQGIS Interpolation on Curved Grid (River DEMs)How to create automatic parking baysShortest path creation between two linesclipping layer using query builder in QGISFinding which side of closest polyline point lies on in QGIS?Create centerline from multi-digitized roadway lines Qgis 2.18Getting bathymetric contours confined only within river banks using QGIS?

                                Image
                                Calculating the number of coins in money change How could chocolate be as addictive as heroin? What do you call a plan that's an alternative plan in case your initial plan fails? Python - Fishing Simulator Simulating Exploding Dice Active filter with series inductor and resistor - do these exist? How can I protect witches in combat who wear limited clothing? Am I ethically obligated to go into work on an off day if the reason is sudden? Format single node in tikzcd Didn't get enough time to take a Coding Test - what to do now? Why can't wing-mounted spoilers be used to steepen approaches? How is simplicity better than precision and clarity in prose? Is there a trick to getting spices to fix to nuts? What can I do if neighbor is blocking my solar panels intentionally? Hiding Certain Lines on Table Wolves and sheep Make it rain characters Can the prologue be the backstory of your main character? Difference between はじめる and ...
                                Read more

                                What is the result of assigning to std::vector::begin()? The Next CEO of Stack OverflowWhat are the differences between a pointer variable and a reference variable in C++?What does the explicit keyword mean?Concatenating two std::vectorsHow to find out if an item is present in a std::vector?Why is “using namespace std” considered bad practice?What is the “-->” operator in C++?What is the easiest way to initialize a std::vector with hardcoded elements?What is The Rule of Three?What are the basic rules and idioms for operator overloading?Why are std::begin and std::end “not memory safe”?

                                Image
                                Is there a way to save my career from absolute disaster? Why didn't Khan get resurrected in the Genesis Explosion? How to make a variable always equal to the result of some calculations? What can we do to stop prior company from asking us questions? How do we know the LHC results are robust? How does the mv command work with external drives? What is ( CFMCC ) on ILS approach chart? Between two walls Should I tutor a student who I know has cheated on their homework? How do scammers retract money, while you can’t? What happens if you roll doubles 3 times then land on "Go to jail?" What is the result of assigning to std::vector<T>::begin()? How to count occurrences of text in a file? What was the first Unix version to run on a microcomputer? Return the Closest Prime Number How did people program for Consoles with multiple CPUs? What does convergence in distribution "in the Gromov–Hausdorff" sense mean? How should I support th...
                                Read more