A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

A region R, in the first quadrant only, is enclosed by y=x^3 and y=cubed root of x. find the volume of the solid obtained by revolving the region R about x=-2.

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

    First you have to imagine and draw a rough of what these would look like. You would find examples of these functions in the first chap of a calculus book or put them in a calculator

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

    okay i imagined it and drew a picture. what do i do next?

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

    Then you find the boundaries of integration (it might be obvious, it starts at 0) but set x^3=cube root of x; solve for x. The points tell you where y=x^3 and y=cube root x intersect (boundaries of integration)

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

    ehhh i tried but i dont know how to find the boundaries. i got x^3-sq root of x=0 but i dont know what that would make x equal?

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

    x^3=cube root of x The problem is the cube root sign. Just cube each side of the eq (x^3)^3=(cube root of x)^3

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

    okay i got x^9-x^2

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

    how do i factor that?

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

    Good. but you are off a little. It should be x^9-x=0 Both x^9 and x have a common factor of x, so you have to pull it out

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

    but if i square the squareroot of x, isnt is x^2?

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

    Actually if you square the square root of x, you get x; likewise cube the cube root you get x

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

    ohhhh okay sorry i got it!

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

    So, you have a lot of catching up, I'm going to go fast because I have to go. So the boundaries are 0 to 1

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

    okay next?

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

    You are going to be using washer method

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

    Radius of big washer is x^3 +2 radius of small washer is cube root of x +2

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

    okay ill try that!

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

    Integrate from 0 to 1 [{(x^3+2)^2}pi - {(cube rooot x +2)^2}pi]

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

    okay i will do that now. whats the final answer?

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

    Haven't work it out. Setting it up is the fun part. Integrating is the dirty work. I left the dirty work for you.

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

    okay thanksss for all the help!

  21. 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.