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?
Is it professional to write unrelated content in an almost-empty email?
sp_blitzCache results Memory grants
What was the first Unix version to run on a microcomputer?
Between two walls
Why didn't Khan get resurrected in the Genesis Explosion?
Is HostGator storing my password in plaintext?
Why do remote companies require working in the US?
Is it my responsibility to learn a new technology in my own time my employer wants to implement?
Why do we use the plural of movies in this phrase "We went to the movies last night."?
Contours of a clandestine nature
How to invert MapIndexed on a ragged structure? How to construct a tree from rules?
Why do professional authors make "consistency" mistakes? And how to avoid them?
Received an invoice from my ex-employer billing me for training; how to handle?
Why has the US not been more assertive in confronting Russia in recent years?
If a black hole is created from light, can this black hole then move at speed of light?
How do I make a variable always equal to the result of some calculations?
Does it take more energy to get to Venus or to Mars?
Why does standard notation not preserve intervals (visually)
What happened in Rome, when the western empire "fell"?
Has this building technique been used in an official set?
What is ( CFMCC ) on ILS approach chart?
Is there a difference between "Fahrstuhl" and "Aufzug"
How did the Bene Gesserit know how to make a Kwisatz Haderach?
What can we do to stop prior company from asking us questions?
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?
$begingroup$
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
edited 28 mins ago
Peter Mortensen
565310
asked 6 hours ago
McAMcA
204
$endgroup$
add a comment |
$begingroup$
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
edited 28 mins ago
Peter Mortensen
565310
asked 6 hours ago
McAMcA
204
$endgroup$
$begingroup$
Is this $$x=5+frac92t^3,y=4+3t^9/2$$?
$endgroup$
– Dr. Sonnhard Graubner
6 hours ago
add a comment |
$begingroup$
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
edited 28 mins ago
Peter Mortensen
565310
asked 6 hours ago
McAMcA
204
$endgroup$
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
edited 28 mins ago
Peter Mortensen
565310
asked 6 hours ago
McAMcA
204
edited 28 mins ago
Peter Mortensen
565310
asked 6 hours ago
McAMcA
204
edited 28 mins ago
Peter Mortensen
565310
edited 28 mins ago
Peter Mortensen
565310
edited 28 mins ago
Peter Mortensen
565310
565310
asked 6 hours ago
McAMcA
204
asked 6 hours ago
McAMcA
204
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
add a comment |
$begingroup$
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
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
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
$$
int_1^9 frac 9 2 sqrtv dv = 78.
$$
answered 6 hours ago
EagleToLearnEagleToLearn
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.
$endgroup$
add a comment |
$begingroup$
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 $f(t)=frac272t^2(1+t^3)^frac12$.
answered 5 hours ago
Matt A PeltoMatt A Pelto
2,667621
$endgroup$
add a comment |
$begingroup$
You must use the formula $$int_0^2sqrtleft(fracdxdtright)^2+left(fracdydtright)^2dt$$
$$dx=frac923t^2dt$$ and $$dy=3cdot frac92t^7/2dt$$
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
$endgroup$
add a comment |
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
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
$begingroup$
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
$$
int_1^9 frac 9 2 sqrtv dv = 78.
$$
answered 6 hours ago
EagleToLearnEagleToLearn
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.
$endgroup$
add a comment |
$begingroup$
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
$$
int_1^9 frac 9 2 sqrtv dv = 78.
$$
answered 6 hours ago
EagleToLearnEagleToLearn
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.
$endgroup$
add a comment |
$begingroup$
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
$$
int_1^9 frac 9 2 sqrtv dv = 78.
$$
answered 6 hours ago
EagleToLearnEagleToLearn
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.
$endgroup$
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
$$
int_1^9 frac 9 2 sqrtv dv = 78.
$$
answered 6 hours ago
EagleToLearnEagleToLearn
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.
answered 6 hours ago
EagleToLearnEagleToLearn
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.
answered 6 hours ago
EagleToLearnEagleToLearn
233
answered 6 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.
add a comment |
add a comment |
$begingroup$
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 $f(t)=frac272t^2(1+t^3)^frac12$.
answered 5 hours ago
Matt A PeltoMatt A Pelto
2,667621
$endgroup$
add a comment |
$begingroup$
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 $f(t)=frac272t^2(1+t^3)^frac12$.
answered 5 hours ago
Matt A PeltoMatt A Pelto
2,667621
$endgroup$
add a comment |
$begingroup$
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 $f(t)=frac272t^2(1+t^3)^frac12$.
answered 5 hours ago
Matt A PeltoMatt A Pelto
2,667621
$endgroup$
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 $f(t)=frac272t^2(1+t^3)^frac12$.
answered 5 hours ago
Matt A PeltoMatt A Pelto
2,667621
edited 5 hours ago
answered 5 hours ago
Matt A PeltoMatt A Pelto
2,667621
answered 5 hours ago
Matt A PeltoMatt A Pelto
2,667621
answered 5 hours ago
Matt A PeltoMatt A Pelto
2,667621
2,667621
add a comment |
add a comment |
$begingroup$
You must use the formula $$int_0^2sqrtleft(fracdxdtright)^2+left(fracdydtright)^2dt$$
$$dx=frac923t^2dt$$ and $$dy=3cdot frac92t^7/2dt$$
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
$endgroup$
add a comment |
$begingroup$
You must use the formula $$int_0^2sqrtleft(fracdxdtright)^2+left(fracdydtright)^2dt$$
$$dx=frac923t^2dt$$ and $$dy=3cdot frac92t^7/2dt$$
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
$endgroup$
add a comment |
$begingroup$
You must use the formula $$int_0^2sqrtleft(fracdxdtright)^2+left(fracdydtright)^2dt$$
$$dx=frac923t^2dt$$ and $$dy=3cdot frac92t^7/2dt$$
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
$endgroup$
You must use the formula $$int_0^2sqrtleft(fracdxdtright)^2+left(fracdydtright)^2dt$$
$$dx=frac923t^2dt$$ and $$dy=3cdot frac92t^7/2dt$$
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
answered 6 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
78.2k42867
add a comment |
add a comment |
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.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
$begingroup$
Is this $$x=5+frac92t^3,y=4+3t^9/2$$?
$endgroup$
– Dr. Sonnhard Graubner
6 hours ago