How do you evaluate an integral using stokes theorem if the curve given is a unit circle in a plane z=α [closed]

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
1
down vote

favorite












So, C is given as a unit circle in the plane z=α, how would I evaluate this when the formula for stokes asks for the normal vector of a curve but given a slice of a cylinder?




multivariable-calculus




share|cite|improve this question











closed as off-topic by Xander Henderson, Adrian Keister, José Carlos Santos, Jyrki Lahtonen, Lord Shark the Unknown Jul 31 at 14:09


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Please take the time to formulate your problem completely. We are no clairvoyants.
    – Christian Blatter
    Jul 30 at 7:42














up vote
1
down vote

favorite












So, C is given as a unit circle in the plane z=α, how would I evaluate this when the formula for stokes asks for the normal vector of a curve but given a slice of a cylinder?




multivariable-calculus




share|cite|improve this question











closed as off-topic by Xander Henderson, Adrian Keister, José Carlos Santos, Jyrki Lahtonen, Lord Shark the Unknown Jul 31 at 14:09


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Please take the time to formulate your problem completely. We are no clairvoyants.
    – Christian Blatter
    Jul 30 at 7:42












up vote
1
down vote

favorite









up vote
1
down vote

favorite











So, C is given as a unit circle in the plane z=α, how would I evaluate this when the formula for stokes asks for the normal vector of a curve but given a slice of a cylinder?




multivariable-calculus




share|cite|improve this question











So, C is given as a unit circle in the plane z=α, how would I evaluate this when the formula for stokes asks for the normal vector of a curve but given a slice of a cylinder?





multivariable-calculus





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 30 at 6:17









edmonda7

163




163




closed as off-topic by Xander Henderson, Adrian Keister, José Carlos Santos, Jyrki Lahtonen, Lord Shark the Unknown Jul 31 at 14:09


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by Xander Henderson, Adrian Keister, José Carlos Santos, Jyrki Lahtonen, Lord Shark the Unknown Jul 31 at 14:09


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Please take the time to formulate your problem completely. We are no clairvoyants.
    – Christian Blatter
    Jul 30 at 7:42
















  • Please take the time to formulate your problem completely. We are no clairvoyants.
    – Christian Blatter
    Jul 30 at 7:42















Please take the time to formulate your problem completely. We are no clairvoyants.
– Christian Blatter
Jul 30 at 7:42




Please take the time to formulate your problem completely. We are no clairvoyants.
– Christian Blatter
Jul 30 at 7:42










1 Answer
1






active

oldest

votes

















up vote
1
down vote













The Stokes Theorem states that
$$oint_C vecF cdot dvecr = iint_S nabla times vecF cdot dvecS = iint_S nabla times vecF cdot vecn; dS, $$
where $S$ is any surface bounded by $C$, with normal unit vector $vecn$.



In your case, $C$ is a unit circle in the plane $z=alpha$, so a good choice is to consider the surface $S$ as the disc inside $C$, that is :
beginalign
&x = r cos theta \
&y = r sin theta quad quad mboxwithquad 0le r le 1, ; 0le theta le 2 pi\
&z= alpha
endalign



The normal unit vector $vecn$ is trivially $(0,0,1)$, which should simplify calculations.






share|cite|improve this answer




























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote













    The Stokes Theorem states that
    $$oint_C vecF cdot dvecr = iint_S nabla times vecF cdot dvecS = iint_S nabla times vecF cdot vecn; dS, $$
    where $S$ is any surface bounded by $C$, with normal unit vector $vecn$.



    In your case, $C$ is a unit circle in the plane $z=alpha$, so a good choice is to consider the surface $S$ as the disc inside $C$, that is :
    beginalign
    &x = r cos theta \
    &y = r sin theta quad quad mboxwithquad 0le r le 1, ; 0le theta le 2 pi\
    &z= alpha
    endalign



    The normal unit vector $vecn$ is trivially $(0,0,1)$, which should simplify calculations.






    share|cite|improve this answer

























      up vote
      1
      down vote













      The Stokes Theorem states that
      $$oint_C vecF cdot dvecr = iint_S nabla times vecF cdot dvecS = iint_S nabla times vecF cdot vecn; dS, $$
      where $S$ is any surface bounded by $C$, with normal unit vector $vecn$.



      In your case, $C$ is a unit circle in the plane $z=alpha$, so a good choice is to consider the surface $S$ as the disc inside $C$, that is :
      beginalign
      &x = r cos theta \
      &y = r sin theta quad quad mboxwithquad 0le r le 1, ; 0le theta le 2 pi\
      &z= alpha
      endalign



      The normal unit vector $vecn$ is trivially $(0,0,1)$, which should simplify calculations.






      share|cite|improve this answer























        up vote
        1
        down vote










        up vote
        1
        down vote









        The Stokes Theorem states that
        $$oint_C vecF cdot dvecr = iint_S nabla times vecF cdot dvecS = iint_S nabla times vecF cdot vecn; dS, $$
        where $S$ is any surface bounded by $C$, with normal unit vector $vecn$.



        In your case, $C$ is a unit circle in the plane $z=alpha$, so a good choice is to consider the surface $S$ as the disc inside $C$, that is :
        beginalign
        &x = r cos theta \
        &y = r sin theta quad quad mboxwithquad 0le r le 1, ; 0le theta le 2 pi\
        &z= alpha
        endalign



        The normal unit vector $vecn$ is trivially $(0,0,1)$, which should simplify calculations.






        share|cite|improve this answer













        The Stokes Theorem states that
        $$oint_C vecF cdot dvecr = iint_S nabla times vecF cdot dvecS = iint_S nabla times vecF cdot vecn; dS, $$
        where $S$ is any surface bounded by $C$, with normal unit vector $vecn$.



        In your case, $C$ is a unit circle in the plane $z=alpha$, so a good choice is to consider the surface $S$ as the disc inside $C$, that is :
        beginalign
        &x = r cos theta \
        &y = r sin theta quad quad mboxwithquad 0le r le 1, ; 0le theta le 2 pi\
        &z= alpha
        endalign



        The normal unit vector $vecn$ is trivially $(0,0,1)$, which should simplify calculations.







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Jul 30 at 9:01









        Kuifje

        6,8112523




        6,8112523












            Comments

            Post a Comment

            Popular posts from this blog

            What is the equation of a 3D cone with generalised tilt?

            Image
            Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin $(0,0,0)$ - I was wondering if anyone could give me a more generalized cone equation for a cone in any position in 3D space 3d share | cite | improve this question edited Jul 25 '16 at 0:05 ervx 9,425 3 13 36 asked Jul 24 '16 at 15:38 Charlene 11 2 2 Welcome to Math.SE! Could you please explain a few things to help people give an answer useful to you: 1. What do you mean by "generalized tilt"? 2. Are you asking about a right circular cone? Does the angle at the vertex matter? 3. What form of answer (implicit, parametric...?) are you looking for? 4. If this is homework, what tools do you have available, an...
            Read more

            Relationship between determinant of matrix and determinant of adjoint?

            Image
            Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite We are studying adjoints in class, and I was curious if there is a relationship between the determinant of matrix A, and the determinant of the adjoint of matrix A? I assume there would be a relationship because finding the adjoint requires creating a cofactor matrix and then transposing it. linear-algebra determinant adjoint-operators share | cite | improve this question asked Nov 17 '17 at 17:32 CluelessCoder 32 5 For a square matrix $A$ of order $n$, we have $A(operatornameadj A)=(operatornameadj A)A=|A|I_n$ where $I_n$ is the identity matrix of order $n$. This should tell you about the determinant of the adjoint in terms of that of $A$ (use multiplicative property and other elementary properties of determinants). – Prasun Biswas Nov 17 '17 at 17:35 1 @CluelessCoder: see here: math.stackexchange.com/questions/516127/…...
            Read more

            Color the edges and diagonals of a regular polygon

            Image
            Clash Royale CLAN TAG #URR8PPP up vote 5 down vote favorite 1 Here is the problem: For what $n$ is it possible to color the edges and diagonals of an $n$-side regular polygon with $dfracbinomn23$ colors, such that you use every color exactly three times and for every color the three segments (edges or diagonals) with that color form a triangle? Trivially $nequiv 0 text or 1 pmod3$. I can also prove that if the statement is true for $k$ than it is true for $3k$ as well. How to finish? Please help! Thanks combinatorial-geometry share | cite | improve this question edited Aug 6 at 21:57 alcana 118 4 asked Aug 6 at 21:15 Leo Gardner 356 11 Even assuming "polyhpn" in the title is a typo for polygon , it is unclear what you mean by "the edges and sides". Aren't the side of a regular polygon the same as the edges? A regular $n$-sided polygon has $n$ edges. – hardmath Aug 6 at 21:20 3 $n$ ne...
            Read more