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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
    6 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
    6 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 18 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
    6 hours ago

















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
















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





$begingroup$
Is this $$x=5+frac92t^3,y=4+3t^9/2$$?
$endgroup$
– Dr. Sonnhard Graubner
6 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









      $endgroup$













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        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 6 hours ago









                            Dr. Sonnhard GraubnerDr. Sonnhard Graubner

                            78.2k42867




                            78.2k42867



























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