A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Find the volume of the solid formed by rotating the region bounded by: y=x^2+2 and y=x+8 around the line, x=4. Leave the answer in terms of pi.

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

    idk

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

    lolz

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

    so what you are basically doing is to find the volume of the washer (I usually call it a ring) and integrate it. what do you think the integrand is ?

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

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

    if you see that the volume of each ring(washer) has a volume V = 2pi ( (4-sqrt(y-2))^2 - (4-(y-8))^2) dx so the integration will be\[2\pi \int\limits (4-\sqrt(y-2))^2- (4-(y-8))^2dx\]

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

    oops, I meant dy

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

    now all you have to do is to figure out the limit of integration

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

    the bottom of the parabola starts at y = 2 and it ends at y = 11 so the limit of integration is from 2 to 11

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

    once you integrate it you are done :)

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

    If you would like, try using the shell method, which is also a good choice for this one :)

  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.