Fdtxjr

Does the Linux kernel need a file system to run?

When were female captains banned from Starfleet?

Why does AES have exactly 10 rounds for a 128-bit key, 12 for 192 bits and 14 for a 256-bit key size?

I found an audio circuit and I built it just fine, but I find it a bit too quiet. How do I amplify the output so that it is a bit louder?

Quoting Keynes in a lecture

Review your own paper in Mathematics

Does the reader need to like the PoV character?

Shouldn’t conservatives embrace universal basic income?

Is there a nicer/politer/more positive alternative for "negates"?

"It doesn't matter" or "it won't matter"?

Why can't the Brexit deadlock in the UK parliament be solved with a plurality vote?

Is my low blitz game drawing rate at www.chess.com an indicator that I am weak in chess?

PTIJ: Why is Haman obsessed with Bose?

How to make money from a browser who sees 5 seconds into the future of any web page?

Why is so much work done on numerical verification of the Riemann Hypothesis?

Mimic lecturing on blackboard, facing audience

Multiplicative persistence

C++ check if statement can be evaluated constexpr

Why is the "ls" command showing permissions of files in a FAT32 partition?

How could a planet have erratic days?

How would you translate "more" for use as an interface button?

Can you use Vicious Mockery to win an argument or gain favours?

Is there a RAID 0 Equivalent for RAM?

Biological Blimps: Propulsion

Evaluate$int_SvecF.dvecS$ where S is the surface of the plane $2x+y=4$ in the first octant cut off by the plane $z=4$

Use the Stokes' Theorem to find the work of the vector field $ overrightarrowF$Where did I got wrong with this surface integralSurface Integral for the planeVerify the divergence theorem for $vecF=xhati-y^2hatj+z^2hatk$ over the region bounded by $x^2+y^2=4,z=0,z=4$Integral without Divergence Theoremstokes theorem integral around a sphere and planeIs $nablacdothatfracrr^3=-frac1r^4+frac1r4pideltavecr$ correct?Computing $int_S vecF.hatn,dS$ where $S:(x,y,z)in R^3:x^2+y^2+2z=2,zgeq 0$Surface integral confusion about boundariesSurface integral over a cone above the xy plane

0

$begingroup$

Question Evaluate$int_SvecF.dvecS$ where$vecF$
= y$hati$ +$2x$$hatj$-z$hatk$ and S is the surface of
the plane $2x+y=4$ in the first octant cut off by the plane $z=4$

My Approach $hatn=fracnabla smidnabla smid=frac1sqrt5left(2hati+hatjright)$
and $dS =fracdxdymidhatn.hatjmid=sqrt5 dxdy$

$vecFcdothatn=frac2sqrt5left(x+yright)$

$vecFcdothatndS=frac2sqrt5left(x+yright)$$sqrt5
dxdy=2left(x+yright)dxdy$

Now i can't decide the region of integral$int_S2left(x+yright)dxdy$

Book's Approach my book uses this formula for $dS$

$$dS =fracdxdzmidhatn.hatjmid=sqrt5 dxdz$$

Is my formula wrong? Or are both formulas correct?

If both formulas are correct then why my method is not giving the
right answer?

vector-analysis surface-integrals

share|cite|improve this question

edited Dec 20 '17 at 12:39

Mohan Sharma

asked Dec 20 '17 at 12:25

Mohan SharmaMohan Sharma

564213

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  For surface integral in vector fields you need to specify the orientation of the plane right.
  $endgroup$
  – user122049
  Dec 20 '17 at 12:39
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @user122049 i am not good at physics and i do not know what is orientation of vector fields and how it is connected to this problem
  $endgroup$
  – Mohan Sharma
  Dec 20 '17 at 12:42
  

  
  
  
  

add a comment | 

0

$begingroup$

Question Evaluate$int_SvecF.dvecS$ where$vecF$
= y$hati$ +$2x$$hatj$-z$hatk$ and S is the surface of
the plane $2x+y=4$ in the first octant cut off by the plane $z=4$

My Approach $hatn=fracnabla smidnabla smid=frac1sqrt5left(2hati+hatjright)$
and $dS =fracdxdymidhatn.hatjmid=sqrt5 dxdy$

$vecFcdothatn=frac2sqrt5left(x+yright)$

$vecFcdothatndS=frac2sqrt5left(x+yright)$$sqrt5
dxdy=2left(x+yright)dxdy$

Now i can't decide the region of integral$int_S2left(x+yright)dxdy$

Book's Approach my book uses this formula for $dS$

$$dS =fracdxdzmidhatn.hatjmid=sqrt5 dxdz$$

Is my formula wrong? Or are both formulas correct?

If both formulas are correct then why my method is not giving the
right answer?

vector-analysis surface-integrals

share|cite|improve this question

edited Dec 20 '17 at 12:39

Mohan Sharma

asked Dec 20 '17 at 12:25

Mohan SharmaMohan Sharma

564213

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  For surface integral in vector fields you need to specify the orientation of the plane right.
  $endgroup$
  – user122049
  Dec 20 '17 at 12:39
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @user122049 i am not good at physics and i do not know what is orientation of vector fields and how it is connected to this problem
  $endgroup$
  – Mohan Sharma
  Dec 20 '17 at 12:42
  

  
  
  
  

add a comment | 

$begingroup$

Question Evaluate$int_SvecF.dvecS$ where$vecF$
= y$hati$ +$2x$$hatj$-z$hatk$ and S is the surface of
the plane $2x+y=4$ in the first octant cut off by the plane $z=4$

My Approach $hatn=fracnabla smidnabla smid=frac1sqrt5left(2hati+hatjright)$
and $dS =fracdxdymidhatn.hatjmid=sqrt5 dxdy$

$vecFcdothatn=frac2sqrt5left(x+yright)$

$vecFcdothatndS=frac2sqrt5left(x+yright)$$sqrt5
dxdy=2left(x+yright)dxdy$

Now i can't decide the region of integral$int_S2left(x+yright)dxdy$

Book's Approach my book uses this formula for $dS$

$$dS =fracdxdzmidhatn.hatjmid=sqrt5 dxdz$$

Is my formula wrong? Or are both formulas correct?

If both formulas are correct then why my method is not giving the
right answer?

vector-analysis surface-integrals

share|cite|improve this question

edited Dec 20 '17 at 12:39

Mohan Sharma

asked Dec 20 '17 at 12:25

Mohan SharmaMohan Sharma

564213

$endgroup$

share|cite|improve this question

edited Dec 20 '17 at 12:39

Mohan Sharma

asked Dec 20 '17 at 12:25

Mohan SharmaMohan Sharma

564213

share|cite|improve this question

edited Dec 20 '17 at 12:39

Mohan Sharma

asked Dec 20 '17 at 12:25

Mohan SharmaMohan Sharma

564213

asked Dec 20 '17 at 12:25

Mohan SharmaMohan Sharma

564213

asked Dec 20 '17 at 12:25

Mohan SharmaMohan Sharma

564213

1 Answer
1

active

oldest

votes

1

$begingroup$

The standard way is to parametrise the surface. The surface can be parametrised in the following way: $mathbfr(u,v)=langle u, 4-2u, v rangle$, where $uin (0,2)$ and $vin(0,4)$. Then, take partial derivatives $mathbfr_u=langle 1,-2,0rangle$ and $mathbfr_v=langle 0, 0, 1rangle$; consequently, $mathbfr_utimesmathbfr_v=langle -2, -1, 0rangle$. This will give you one choice of normal vector $mathbfn$, but whether this is the correct orientation, it is dependent on the question(the other being $-mathbfn$). That is why I ask for the correct orientation.

We compute the surface integral in the following way: $int_SmathbfF mathrmdS=iint_DmathbfFcdot(mathbfr_utimesmathbfr_v)mathrmdA$, where $D$ is comprised of all the $(u,v)$ in domain. Here, the equation gives $iint_Dlangle 4-2u,2u,-vranglecdotlangle -2, -1, 0ranglemathrmdA=int_0^4int_0^2(-8+2u)mathrmdumathrmdv=-48$

share|cite|improve this answer

edited Dec 20 '17 at 12:57

answered Dec 20 '17 at 12:52

user122049user122049

811716

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks brother your approach is very much helpful for the many other problems as well.i had seen this method on the internet,but it was not given in my book ,but from now i will always use this method
  $endgroup$
  – Mohan Sharma
  Dec 20 '17 at 13:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Mohan Sharma , I solved this and got +48 .Please tell me the correct answer .
  $endgroup$
  – освящение
  Jan 24 '18 at 12:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Mohan please tell me the answer so that i can correct my approach .
  $endgroup$
  – освящение
  Jan 25 '18 at 6:29
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Abhishek Hi, since the orientation of the surface is not given, both $+48$ and $-48$ are correct answers.
  $endgroup$
  – user122049
  Jan 25 '18 at 10:57
  

  
  
  
  

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
);



);

draft saved

draft discarded

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

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2574415%2fevaluate-int-s-vecf-d-vecs-where-s-is-the-surface-of-the-plane-2xy-4%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

1

$begingroup$

The standard way is to parametrise the surface. The surface can be parametrised in the following way: $mathbfr(u,v)=langle u, 4-2u, v rangle$, where $uin (0,2)$ and $vin(0,4)$. Then, take partial derivatives $mathbfr_u=langle 1,-2,0rangle$ and $mathbfr_v=langle 0, 0, 1rangle$; consequently, $mathbfr_utimesmathbfr_v=langle -2, -1, 0rangle$. This will give you one choice of normal vector $mathbfn$, but whether this is the correct orientation, it is dependent on the question(the other being $-mathbfn$). That is why I ask for the correct orientation.

We compute the surface integral in the following way: $int_SmathbfF mathrmdS=iint_DmathbfFcdot(mathbfr_utimesmathbfr_v)mathrmdA$, where $D$ is comprised of all the $(u,v)$ in domain. Here, the equation gives $iint_Dlangle 4-2u,2u,-vranglecdotlangle -2, -1, 0ranglemathrmdA=int_0^4int_0^2(-8+2u)mathrmdumathrmdv=-48$

share|cite|improve this answer

edited Dec 20 '17 at 12:57

answered Dec 20 '17 at 12:52

user122049user122049

811716

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks brother your approach is very much helpful for the many other problems as well.i had seen this method on the internet,but it was not given in my book ,but from now i will always use this method
  $endgroup$
  – Mohan Sharma
  Dec 20 '17 at 13:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Mohan Sharma , I solved this and got +48 .Please tell me the correct answer .
  $endgroup$
  – освящение
  Jan 24 '18 at 12:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Mohan please tell me the answer so that i can correct my approach .
  $endgroup$
  – освящение
  Jan 25 '18 at 6:29
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Abhishek Hi, since the orientation of the surface is not given, both $+48$ and $-48$ are correct answers.
  $endgroup$
  – user122049
  Jan 25 '18 at 10:57
  

  
  
  
  

add a comment | 

1

$begingroup$

The standard way is to parametrise the surface. The surface can be parametrised in the following way: $mathbfr(u,v)=langle u, 4-2u, v rangle$, where $uin (0,2)$ and $vin(0,4)$. Then, take partial derivatives $mathbfr_u=langle 1,-2,0rangle$ and $mathbfr_v=langle 0, 0, 1rangle$; consequently, $mathbfr_utimesmathbfr_v=langle -2, -1, 0rangle$. This will give you one choice of normal vector $mathbfn$, but whether this is the correct orientation, it is dependent on the question(the other being $-mathbfn$). That is why I ask for the correct orientation.

We compute the surface integral in the following way: $int_SmathbfF mathrmdS=iint_DmathbfFcdot(mathbfr_utimesmathbfr_v)mathrmdA$, where $D$ is comprised of all the $(u,v)$ in domain. Here, the equation gives $iint_Dlangle 4-2u,2u,-vranglecdotlangle -2, -1, 0ranglemathrmdA=int_0^4int_0^2(-8+2u)mathrmdumathrmdv=-48$

share|cite|improve this answer

edited Dec 20 '17 at 12:57

answered Dec 20 '17 at 12:52

user122049user122049

811716

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks brother your approach is very much helpful for the many other problems as well.i had seen this method on the internet,but it was not given in my book ,but from now i will always use this method
  $endgroup$
  – Mohan Sharma
  Dec 20 '17 at 13:15
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Mohan Sharma , I solved this and got +48 .Please tell me the correct answer .
  $endgroup$
  – освящение
  Jan 24 '18 at 12:10
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Mohan please tell me the answer so that i can correct my approach .
  $endgroup$
  – освящение
  Jan 25 '18 at 6:29
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Abhishek Hi, since the orientation of the surface is not given, both $+48$ and $-48$ are correct answers.
  $endgroup$
  – user122049
  Jan 25 '18 at 10:57
  

  
  
  
  

add a comment | 

$begingroup$

The standard way is to parametrise the surface. The surface can be parametrised in the following way: $mathbfr(u,v)=langle u, 4-2u, v rangle$, where $uin (0,2)$ and $vin(0,4)$. Then, take partial derivatives $mathbfr_u=langle 1,-2,0rangle$ and $mathbfr_v=langle 0, 0, 1rangle$; consequently, $mathbfr_utimesmathbfr_v=langle -2, -1, 0rangle$. This will give you one choice of normal vector $mathbfn$, but whether this is the correct orientation, it is dependent on the question(the other being $-mathbfn$). That is why I ask for the correct orientation.

We compute the surface integral in the following way: $int_SmathbfF mathrmdS=iint_DmathbfFcdot(mathbfr_utimesmathbfr_v)mathrmdA$, where $D$ is comprised of all the $(u,v)$ in domain. Here, the equation gives $iint_Dlangle 4-2u,2u,-vranglecdotlangle -2, -1, 0ranglemathrmdA=int_0^4int_0^2(-8+2u)mathrmdumathrmdv=-48$

share|cite|improve this answer

edited Dec 20 '17 at 12:57

answered Dec 20 '17 at 12:52

user122049user122049

811716

$endgroup$

share|cite|improve this answer

edited Dec 20 '17 at 12:57

answered Dec 20 '17 at 12:52

user122049user122049

811716

answered Dec 20 '17 at 12:52

user122049user122049

811716

answered Dec 20 '17 at 12:52

user122049user122049

811716