Determine $int_C Fcdot dx$ where $F(x,y,z)=(z,-y,x)$ and $C$ is the line segment from $(5,0,2)$ to $(5,3,4)$ Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Use Stokes' Theorem to evaluate integralEvaluate the line integral $int_C x^2 dx+(x+y)dy $Line integrals and path independenceFind a plane that passes through a given point and contains a given lineParametric line segment in 3-spaceEvaluate the line integral $int_C (x^2-y+3z);ds$Maximizing the line integral over a line segmentWork on a line segment - Final stepFinding the distance between a point and line (3-D)Formula of curvature not defined in arc length
Multi tool use
Sum letters are not two different
How does light 'choose' between wave and particle behaviour?
How to write this math term? with cases it isn't working
Is it possible for SQL statements to execute concurrently within a single session in SQL Server?
Is a ledger board required if the side of my house is wood?
What does it mean that physics no longer uses mechanical models to describe phenomena?
Can a new player join a group only when a new campaign starts?
How to install press fit bottom bracket into new frame
How to compare two different files line by line in unix?
How often does castling occur in grandmaster games?
Why should I vote and accept answers?
Why is it faster to reheat something than it is to cook it?
What is "gratricide"?
Should I use a zero-interest credit card for a large one-time purchase?
How were pictures turned from film to a big picture in a picture frame before digital scanning?
What is the topology associated with the algebras for the ultrafilter monad?
Crossing US/Canada Border for less than 24 hours
SF book about people trapped in a series of worlds they imagine
What is a fractional matching?
What is this clumpy 20-30cm high yellow-flowered plant?
Take 2! Is this homebrew Lady of Pain warlock patron balanced?
Is there a kind of relay that only consumes power when switching?
What is the difference between globalisation and imperialism?
Do I really need to have a message in a novel to appeal to readers?
Determine $int_C Fcdot dx$ where $F(x,y,z)=(z,-y,x)$ and $C$ is the line segment from $(5,0,2)$ to $(5,3,4)$
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Use Stokes' Theorem to evaluate integralEvaluate the line integral $int_C x^2 dx+(x+y)dy $Line integrals and path independenceFind a plane that passes through a given point and contains a given lineParametric line segment in 3-spaceEvaluate the line integral $int_C (x^2-y+3z);ds$Maximizing the line integral over a line segmentWork on a line segment - Final stepFinding the distance between a point and line (3-D)Formula of curvature not defined in arc length
$begingroup$
So first thing I did was parametrize the line. I used $gamma(t)=(5,t,2+frac23t)$ For $tin [0,3]$
I then have $F(gamma(t))=(2+frac23t,-t,5)$
and $dotgamma(t)=(0,1,frac23)$
Then $int_C Fdx=int_0^3 langle F,Trangle=int_0^3 -t+frac103dt=-frac23$
I'm pretty sure my parametrization is incorrect as I dont think I should get this negative.
multivariable-calculus
asked Mar 27 at 17:06
AColoredReptileAColoredReptile
401210
$endgroup$
add a comment |
$begingroup$
So first thing I did was parametrize the line. I used $gamma(t)=(5,t,2+frac23t)$ For $tin [0,3]$
I then have $F(gamma(t))=(2+frac23t,-t,5)$
and $dotgamma(t)=(0,1,frac23)$
Then $int_C Fdx=int_0^3 langle F,Trangle=int_0^3 -t+frac103dt=-frac23$
I'm pretty sure my parametrization is incorrect as I dont think I should get this negative.
multivariable-calculus
asked Mar 27 at 17:06
AColoredReptileAColoredReptile
401210
$endgroup$
add a comment |
$begingroup$
So first thing I did was parametrize the line. I used $gamma(t)=(5,t,2+frac23t)$ For $tin [0,3]$
I then have $F(gamma(t))=(2+frac23t,-t,5)$
and $dotgamma(t)=(0,1,frac23)$
Then $int_C Fdx=int_0^3 langle F,Trangle=int_0^3 -t+frac103dt=-frac23$
I'm pretty sure my parametrization is incorrect as I dont think I should get this negative.
multivariable-calculus
asked Mar 27 at 17:06
AColoredReptileAColoredReptile
401210
$endgroup$
So first thing I did was parametrize the line. I used $gamma(t)=(5,t,2+frac23t)$ For $tin [0,3]$
I then have $F(gamma(t))=(2+frac23t,-t,5)$
and $dotgamma(t)=(0,1,frac23)$
Then $int_C Fdx=int_0^3 langle F,Trangle=int_0^3 -t+frac103dt=-frac23$
I'm pretty sure my parametrization is incorrect as I dont think I should get this negative.
multivariable-calculus
multivariable-calculus
asked Mar 27 at 17:06
AColoredReptileAColoredReptile
401210
asked Mar 27 at 17:06
AColoredReptileAColoredReptile
401210
edited Mar 27 at 17:12
AColoredReptile
asked Mar 27 at 17:06
AColoredReptileAColoredReptile
401210
asked Mar 27 at 17:06
AColoredReptileAColoredReptile
401210
asked Mar 27 at 17:06
AColoredReptileAColoredReptile
401210
401210
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Your calculations are correct; except the last step of the integration, which is $$int_0^3left(frac103-tright)mathrm dt=frac112.$$
answered Mar 27 at 17:11
st.mathst.math
1,268115
$endgroup$
add a comment |
Your Answer
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%2f3164785%2fdetermine-int-c-f-cdot-dx-where-fx-y-z-z-y-x-and-c-is-the-line-segme%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Your calculations are correct; except the last step of the integration, which is $$int_0^3left(frac103-tright)mathrm dt=frac112.$$
answered Mar 27 at 17:11
st.mathst.math
1,268115
$endgroup$
add a comment |
$begingroup$
Your calculations are correct; except the last step of the integration, which is $$int_0^3left(frac103-tright)mathrm dt=frac112.$$
answered Mar 27 at 17:11
st.mathst.math
1,268115
$endgroup$
add a comment |
$begingroup$
Your calculations are correct; except the last step of the integration, which is $$int_0^3left(frac103-tright)mathrm dt=frac112.$$
answered Mar 27 at 17:11
st.mathst.math
1,268115
$endgroup$
Your calculations are correct; except the last step of the integration, which is $$int_0^3left(frac103-tright)mathrm dt=frac112.$$
answered Mar 27 at 17:11
st.mathst.math
1,268115
answered Mar 27 at 17:11
st.mathst.math
1,268115
answered Mar 27 at 17:11
st.mathst.math
1,268115
answered Mar 27 at 17:11
st.mathst.math
1,268115
1,268115
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%2f3164785%2fdetermine-int-c-f-cdot-dx-where-fx-y-z-z-y-x-and-c-is-the-line-segme%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
wesOapDRfnuK,Uds77Bl1pDBjLx0GCCJ93
