A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Let f(x) = the cube root of x. Find the area of the surface generated by revolving the curve y = f(x) around the x-axis, for x ranging from 0 to 1.

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

    Ok, so how did you want to set this up? Disks?

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

    ? disks?

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

    explain all my professor said was

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

    Keep in mind that the derivative of the cube root of x tends to infinity as x tends to 0, so the area will be equal to an improper integral. Be sure that you express your answer so that it is an actual real number, not an expression which evaluates to infinity minus infinity. For example, if the indefinite integral were ln(x) + ln(2/x), you would not want to plug in x = 0, and write the answer as ln(0) + ln(2/0). Instead, you would want to simplify the indefinite integral to ln(x times 2/x) = ln(2).

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

    this is all my professor gave me this is homework and i dont understand it

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

    Keep in mind that the derivative of the cube root of x tends to infinity as x tends to 0, so the area will be equal to an improper integral. Be sure that you express your answer so that it is an actual real number, not an expression which evaluates to infinity minus infinity. For example, if the indefinite integral were ln(x) + ln(2/x), you would not want to plug in x = 0, and write the answer as ln(0) + ln(2/0). Instead, you would want to simplify the indefinite integral to ln(x times 2/x) = ln(2).

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

    explain all my professor said was

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

    sorry, I thought you said volume, not surface area.

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

    do you know how to do this

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

    ??

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

    So how did you set up the integral

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

    Or have you yet.

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

    didnt do it yet but i know this much idk if its right

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

    S = 2π ∫(x = a,b) √(1 + (dy/dx)²) dx Differentiate f(x) = ∛(x) = x^(1/3) to get: f'(x) = (1/3)x^(-2/3) = 1/(3x^(2/3))

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

    \[\frac{d}{dx}x^{1/3} = \frac{1}{3\sqrt[3]{x^2}}\] That's right. So we plug in that for dy/dx in the integral (squaring it) and evaluate it as an improper integral.

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

    ~=1.885

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

    can you explain how you got this because i need the work for it so i can try to understand it all

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

    because ive got a final tomrrow and i sorta need to know this all

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

    \[\lim_{b\rightarrow 0} \int_b^1 \sqrt{1+(\frac{1}{3\sqrt[3]{x^2}})^2} dx \]

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

    so first its S = 2π ∫(x = a,b) √(1 + (dy/dx)²) dx Differentiate f(x) = ∛(x) = x^(1/3) to get: f'(x) = (1/3)x^(-2/3) = 1/(3x^(2/3))

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

    then its the limit as etc.. then its d/dx and then wa because now i still didnt get the answer

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

    Hrm.. I'm not sure that's right.. Seems too awful

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

    Ah. I forgot you multiply the radical by the original f(x). It should be \[\lim_{b\rightarrow 0} \int_b^1 \sqrt[3]{x}\sqrt{1+(\frac{1}{3\sqrt[3]{x^2}})^2} dx\]

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

    That's much better.

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

    so this is in order

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

    so first its S = 2π ∫(x = a,b) √(1 + (dy/dx)²) dx Differentiate f(x) = ∛(x) = x^(1/3) to get: f'(x) = (1/3)x^(-2/3) = 1/(3x^(2/3))

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

    limb→0∫1bx−√31+(13x2−−−√3)2−−−−−−−−−−−−√dx

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

    then

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

    ddxx1/3=13x2−−√3

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

    this doesnt come outto be the same wouldnt d/dx change since the limit changd?

  31. 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.