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

monroe17 Group Title

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=3sqrt(x) and y=3x^2 about the y-axis

  • one year ago
  • one year ago

  • This Question is Closed
  1. NoelGreco Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    What are the points of intersection?

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

    For two functions \(f\) and \(g\) where \(f \ge g\), the volume between \(x=a\) and \(x=b\) by the cylindrical shells method is given by the following formula. You find those bounds by finding the points of intersection of \(f\) and \(g\), presumably. \[V=2\pi \int_a^b x (f-g) dx\]

    • one year ago
  3. monroe17 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    0 and 1 are the points of intersection.. but I can't seem to figure out the function to evaluate the integral at ;/

    • one year ago
  4. NoelGreco Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1361312140525:dw| Each shell is going to have the shape of a rectangle when it is unfolded from the circular shell shape. You are really looking for the volume of that rectangle. V = length X height X thickness The thickness is going to be dx or dy, the height is the difference between the two functions, and the length is the circumference of each shell.

    • one year ago
  5. yakeyglee Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Using the formula, we have \(f=3\sqrt x\) and \(g=3x^2\). So\[V=2\pi \int_a^b x (3 \sqrt x + 3x^2) dx.\]You can simplify and integrate that, yes?

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

    I should have put \(\displaystyle \int_0^1\), but you get the idea.

    • one year ago
  7. monroe17 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    how did you know what f and g were..? do you just assume?

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

    They were the equations you were given (\(f\) is the upper bound and \(g\) is the lower bound). Does that make sense?

    • one year ago
  9. monroe17 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    what defines an upper and lower bound?

    • one year ago
  10. NoelGreco Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I think you want the DIFFERENCE between the two functions in the integrand.

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

    @NoelGreco, I do. Look at the integral again. @monroe17, the upper bound is the function that defines the top part of the bounded area, and the lower bound defines the lower part of the bounded area (look at their positions in the picture you drew).

    • one year ago
  12. NoelGreco Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I looked at both. You have the sum, not the difference.

    • one year ago
  13. NoelGreco Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Just make sure you get \[\frac{ 9\Pi }{ 10 }\]

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

    That is what I meant. \[V=2\pi \int_\color{red}{0}^\color{red}{1} x (3 \sqrt x \color{red}{-} 3x^2) dx.\]

    • 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.