Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    12
    ReputationRep:
    Problem is attached.

    To do the line integral, I need to find F(r(t)), but I don't understand how to express it. For example I looked at the online notes provided here: http://tutorial.math.lamar.edu/Class...torFields.aspx

    I don't understand how F(r(t)) was derived in the first example. I know how to do the rest.

    Name:  vector.jpg
Views: 52
Size:  28.4 KB
    Offline

    20
    ReputationRep:
    (Original post by blah3210)
    Problem is attached.

    To do the line integral, I need to find F(r(t)), but I don't understand how to express it. For example I looked at the online notes provided here: http://tutorial.math.lamar.edu/Class...torFields.aspx

    I don't understand how F(r(t)) was derived in the first example. I know how to do the rest.

    Name:  vector.jpg
Views: 52
Size:  28.4 KB
    Express it as a vector(either in column, row or i, j, k). F is a function taking a 3d vector to a 3d vector. In this case, \vec{F}(\begin{pmatrix}x\\ y\\ z \end{pmatrix}) = \begin{pmatrix}2\sin x \cos x\\0\\2z\end{pmatrix}.

    A general point on the line is \vec{r}(t) = \begin{pmatrix}t \\ t \\ t^2 \end{pmatrix}, so \vec{F}(\vec{r}(t)) = \begin{pmatrix}2\sin t\cos t\\ 0 \\ 2t^2 \end{pmatrix}.
    Offline

    9
    ReputationRep:
    (Original post by blah3210)
    Problem is attached.

    To do the line integral, I need to find F(r(t)), but I don't understand how to express it. For example I looked at the online notes provided here: http://tutorial.math.lamar.edu/Class...torFields.aspx

    I don't understand how F(r(t)) was derived in the first example. I know how to do the rest.

    Name:  vector.jpg
Views: 52
Size:  28.4 KB
    To find F(r(t)) you need to sub in for each of the components for example if F=(2x,x-y,0) and the path parametrised by r(t)=(x(t),y(t),z(t))=(t,2t,t^2) (for some interval of t) then whenever you see an x you need to sub in for the x component of the path so the 2x of the vector field becomes 2t since x(t)=t. Similarly for the other components and we get F(r(t))=(2t,t-2t,0)=(2t,-t,0).

    Hopefully you can see how it works for your example now.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Has a teacher ever helped you cheat?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.