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?
$begingroup$
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
edited 4 hours ago
Matt A Pelto
2,667621
asked 4 hours ago
McAMcA
224
$endgroup$
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 :( Can anyone show me the steps?
calculus parametric
edited 4 hours ago
Matt A Pelto
2,667621
asked 4 hours ago
McAMcA
224
$endgroup$
$begingroup$
Is this $$x=5+frac{9}{2}t^3,y=4+3t^{9/2}$$?
$endgroup$
– Dr. Sonnhard Graubner
4 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 :( Can anyone show me the steps?
calculus parametric
edited 4 hours ago
Matt A Pelto
2,667621
asked 4 hours ago
McAMcA
224
$endgroup$
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
edited 4 hours ago
Matt A Pelto
2,667621
asked 4 hours ago
McAMcA
224
edited 4 hours ago
Matt A Pelto
2,667621
asked 4 hours ago
McAMcA
224
edited 4 hours ago
Matt A Pelto
2,667621
edited 4 hours ago
Matt A Pelto
2,667621
edited 4 hours ago
Matt A Pelto
2,667621
2,667621
asked 4 hours ago
McAMcA
224
asked 4 hours ago
McAMcA
224
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
add a comment |
$begingroup$
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
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
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
$$
int_1^9 frac 9 2 sqrt{v} dv = 78.
$$
answered 4 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 |
$begingroup$
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 $f(t)=frac{27}2t^2(1+t^3)^{frac12}$.
answered 4 hours ago
Matt A PeltoMatt A Pelto
2,667621
$endgroup$
add a comment |
$begingroup$
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 $$dy=3cdot frac{9}{2}t^{7/2}dt$$
answered 4 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%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
$begingroup$
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
$$
int_1^9 frac 9 2 sqrt{v} dv = 78.
$$
answered 4 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
$$
int_0^2 frac{27{{t}^{2}},sqrt{{{t}^{3}}+1}}{2} dt
$$
Then we make the change of variable $v=t^3+1$ to get
$$
int_1^9 frac 9 2 sqrt{v} dv = 78.
$$
answered 4 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
$$
int_0^2 frac{27{{t}^{2}},sqrt{{{t}^{3}}+1}}{2} dt
$$
Then we make the change of variable $v=t^3+1$ to get
$$
int_1^9 frac 9 2 sqrt{v} dv = 78.
$$
answered 4 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
$$
int_0^2 frac{27{{t}^{2}},sqrt{{{t}^{3}}+1}}{2} dt
$$
Then we make the change of variable $v=t^3+1$ to get
$$
int_1^9 frac 9 2 sqrt{v} dv = 78.
$$
answered 4 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 4 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 4 hours ago
EagleToLearnEagleToLearn
233
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.
add a comment |
add a comment |
$begingroup$
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 $f(t)=frac{27}2t^2(1+t^3)^{frac12}$.
answered 4 hours ago
Matt A PeltoMatt A Pelto
2,667621
$endgroup$
add a comment |
$begingroup$
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 $f(t)=frac{27}2t^2(1+t^3)^{frac12}$.
answered 4 hours ago
Matt A PeltoMatt A Pelto
2,667621
$endgroup$
add a comment |
$begingroup$
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 $f(t)=frac{27}2t^2(1+t^3)^{frac12}$.
answered 4 hours ago
Matt A PeltoMatt A Pelto
2,667621
$endgroup$
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 $f(t)=frac{27}2t^2(1+t^3)^{frac12}$.
answered 4 hours ago
Matt A PeltoMatt A Pelto
2,667621
edited 3 hours ago
answered 4 hours ago
Matt A PeltoMatt A Pelto
2,667621
answered 4 hours ago
Matt A PeltoMatt A Pelto
2,667621
answered 4 hours ago
Matt A PeltoMatt A Pelto
2,667621
2,667621
add a comment |
add a comment |
$begingroup$
You must use the formula $$int_{0}^{2}sqrt{left(frac{dx}{dt}right)^2+left(frac{dy}{dt}right)^2}dt$$
$$dx=frac{9}{2}3t^2dt$$ and $$dy=3cdot frac{9}{2}t^{7/2}dt$$
answered 4 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
$endgroup$
add a comment |
$begingroup$
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 $$dy=3cdot frac{9}{2}t^{7/2}dt$$
answered 4 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
$endgroup$
add a comment |
$begingroup$
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 $$dy=3cdot frac{9}{2}t^{7/2}dt$$
answered 4 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
$endgroup$
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 $$dy=3cdot frac{9}{2}t^{7/2}dt$$
answered 4 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
answered 4 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
answered 4 hours ago
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
78.2k42867
answered 4 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%2fcalculus-parametric-curve-length%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 $$x=5+frac{9}{2}t^3,y=4+3t^{9/2}$$?
$endgroup$
– Dr. Sonnhard Graubner
4 hours ago