A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Can anyone help me with Multiple Integration? 1 2 ∫ ∫ (1-6x^2y) dxdy 0 0

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its fairly easy

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    let the inner integral by say, J

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[J = \int\limits_{0}^{2} (1-6x^2 y ) dx = [ (x - 2x^3 y ) ] \] evaluated at x=2, then substract it evaluated at x=0

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    remember the inner integral, we have dx on the end, so x is the variable, and we treat y as a constant

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so J = ( [ 2 - 16y] - [ 0] )

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now, let the outer integral be I \[I = \int\limits_{0}^{1} (2-16y) dy = [ 2y -8y^2 ] \] between the limits

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so final answer = ( [ 2(1) -8(1)] - [ 0] ) = -6

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    something interesting to note, we get a negative answer

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    remember the geometric meaning of the double integral, "the volume between the surface and the xy plane", well , in this case our surface is below the xy plane over our domain of integration , thus why we get a "negative volume"

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wow thanks :) you're awesome ! :D

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.