Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

3psilon

rotate the region bounded by y = 6 - 2x - x^2 and y = x+6 about the line y=3

  • one year ago
  • one year ago

  • This Question is Closed
  1. 3psilon
    Best Response
    You've already chosen the best response.
    Medals 0

    My answer differs from that of my teacher's. Can someone just show me the integral

    • one year ago
  2. zepdrix
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you provide the teacher's answer a sec? I wanna see if I made some terrible mistake before I post this integral :P

    • one year ago
  3. 3psilon
    Best Response
    You've already chosen the best response.
    Medals 0

    ok ok

    • one year ago
  4. 3psilon
    Best Response
    You've already chosen the best response.
    Medals 0

    • one year ago
  5. 3psilon
    Best Response
    You've already chosen the best response.
    Medals 0

    Problem 21 part D

    • one year ago
  6. zepdrix
    Best Response
    You've already chosen the best response.
    Medals 1

    Hmm this is setup really strangly... Clearly the parabola is our upper function. So why is the parabola being subtracted from the line... This is what I came up with, \[\large \pi \int\limits_{-3}^0 \left[(6-2x-x^2)-3\right]^2-\left[(x+6)-3\right]^2\;dx\] I should look over my work again though.. bit of a tricky problem. I may have made a mistake somewhere.

    • one year ago
  7. 3psilon
    Best Response
    You've already chosen the best response.
    Medals 0

    But I thought the outer radius was at a height 3 plus the parabola function so why wouldn't it be 3+(6-2x-x^2)?

    • one year ago
  8. zepdrix
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1362721421835:dw|So the outer radius \(\large R\) is going to be \(\large y_1-3\). Where \(\large y_1=6-2x-x^2\).

    • one year ago
  9. zepdrix
    Best Response
    You've already chosen the best response.
    Medals 1

    I hope that drawing makes sense... :\ I took a slice and spun it around y=3. And drew some lines to figure out the radius.

    • one year ago
  10. 3psilon
    Best Response
    You've already chosen the best response.
    Medals 0

    It makes sense but can you explain why we subtract 3?

    • one year ago
  11. zepdrix
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1362721856820:dw|That new length is the outer radius.

    • one year ago
  12. zepdrix
    Best Response
    You've already chosen the best response.
    Medals 1

    If we were to draw a disk (not hollowed out) with that radius, it would look like this.|dw:1362722006047:dw| This area of this disk, minus the area of, |dw:1362722103066:dw| Gives us the area of our disk hollowed out,\|dw:1362722226356:dw|[\large A=\pi\left[R^2-r^2\right]\]

    • one year ago
  13. zepdrix
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\large A=\pi\left[R^2-r^2\right]\]

    • one year ago
  14. zepdrix
    Best Response
    You've already chosen the best response.
    Medals 1

    Bah I wish the drawing tool had more functionality :) lol

    • one year ago
  15. 3psilon
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhhh okay okay ! I always had trouble seeing that part! Thank you ! hhha I really appreciate the drawings they helped a lot! Thanks for helping me get ready for my test!

    • one year ago
  16. zepdrix
    Best Response
    You've already chosen the best response.
    Medals 1

    Makes a bit of sense? :D Yay!

    • one year ago
    • Attachments:

See more questions >>>

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.