Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

abtrehearn

  • 3 years ago

I click on Rbrass33's question about setting up an integral, and I get nothing but blank space. Something's terribly amiss.

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

    Is there supposed to be an integrand other than 1, or is the integral used to find the volume of the region? Is the integral supposed to be a single integral of is it supposed to be a multiple integral?

  2. Rbrass33
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey sorry i don't know what wrong

  3. Rbrass33
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but i can post it here :) need help setting up integral. Let W be the region inside the cone z =sqrt(x^2 + y^2) and below the plane z = 1

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

    Looking for volume of region?

  5. Rbrass33
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yupp

  6. Rbrass33
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i was trying to use cylindrical coordinates and i had r is from 0 to 1, theta is from 0 to 2pi and z is from 0 to 1

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

    We can set up the integral using either the disk method or the cylindrical shell method.

  8. Rbrass33
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay which one is easier

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

    Looks like disk method is easier. Dependent variable z goes from 0 1o 1, and we can partition it. In a particular subinterval of length dz is some particular z.

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

    The disk has radius z, so its volume dV is pr*z^2 dz. Since z goes from 0 to 1, \[V =\pi \int\limits_{0}^{1} z ^{2}dz.\]

  11. Rbrass33
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so u don't need to set up a triple integral to find the volume?

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

    What for? Keep it simple.

  13. Rbrass33
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol i like that

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

    Even the cylindrical shell would be easier than the triple integral method. We could do it if we had to, though.

  15. Rbrass33
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks for the help :)

  16. Rbrass33
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i was just looking over the problem again and it says to evaluate the triple integral (1+sqrt(x^2+y^2) dV bound by W= the region inside the cone z =sqrt(x^2 + y^2) and below the plane z = 1

  17. Rbrass33
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    would that still be equal to the volume= integral pi z^2 dz?

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

    Yes.

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

    Yhe integral from 0 to 1, that is.

  20. 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.