Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mattt9

  • 2 years ago

Are you familiar with line integrals in vector fields? if So please help with the question i post below

  • This Question is Closed
  1. mattt9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let C_ij be the boundary of the square [i,i+1]x[j,j+1], oriented clockwise, and \[F = <x^2y^2+2, 3x+y>.\] Calculate \[\sin(\sum_{i=4}^{14}\sum_{j=7}^{17} \int\limits_{C_ij}Fdotdr)\]

  2. mattt9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    where dot is the dot operator not multiplication

  3. mattt9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and F is a vector field which should be in bold (or with an arrow on top), and dr is a vector as well

  4. shaan_iitk
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okk this is of the form \[\int\limits_{}^{} (x^2y^2+2 )dx + \int\limits_{}^{}(3x+y)dy\] .. Now apply greens theorem to get \[\int\limits_{j}^{j+1} \int\limits_{i}^{i+1}(3 - 2x^2y)dxdy\] ... solve this and use summation to find the value.

  5. mattt9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Great! i'll give it a try tomorrow morning thank you

  6. mattt9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    one question though, is there a way that I wouldn't have to integrate that 10 times? like do some terms automatically cancel out somehow?

  7. shaan_iitk
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you don't need to integrate 10 times.. you need to integrate once ...Then you need to sum it 10 times (integration would give you number in terms of i and j)

  8. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.