Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

pdd21

  • one year ago

Calc Problem: Help please! Find the volume of the solid obtained by rotating the region bounded by y=9 x^2, x = 1, and y = 0, about the x-axis.

  • This Question is Closed
  1. pdd21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @campbell_st

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

    ok the the formula for rotating about the x axis is \[V = \pi \int\limits_{a}^{b} y^2 dx\] so the values of a and b are and then y = 0 the corresponding value of x is x = 0... so that means a = 0 and b = 1 the graph looks like |dw:1386823443784:dw| so you are looking at \[V = \pi \int\limits_{0}^{1} (9x^2)^2 dx\] so just simply the (9x^2)^2 then integrate and evaluate between x = 1 and x = 0

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

    hope this helps

  4. pdd21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you so much that helped clear up my confusion! there was another problem I was stuck on, but instead of it being respect to x-axis it's respect to the y-axis. -> Find the volume of the solid obtained by rotating the region bounded by y=x^2 , y = 0, and x = 3, about the y-axis. how do I solve this problem? @campbell_st

  5. pdd21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do i solve it the same?

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

    ok... so find the upper value of the curve at x = 3 so y = 9 this is similar to before |dw:1386823955174:dw| the values of a and b are a = 0 and b = 9 so you are looking at \[V = \pi \int\limits_{a}^{b} x^2 dy\] you have your equation in terms of x^2 so its \[V = \pi \int\limits_{0}^{9} y dy\] hope it makes sense

  7. pdd21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so, \[V=\pi \int\limits_{0}^{9} (x^2)\] I don't seem to be getting the correct answer ;/ @campbell_st

  8. pdd21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    nvm! I caught my mistake! haha

  9. pdd21
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thankk you!(:

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

    well because you are rotating about the y axis you integrate with respect to y \[V = \pi \int\limits_{0}^{9} y dy = 2\pi[\frac{y}{2}]^9_{0}\]

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

    oops forgot the y^2... \[V = \pi \int\limits_{0}^{9} y dy = \pi [\frac{y^2}{2}]^9_{0}\]

  12. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.