A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Consider the solid obtained by rotating the region bounded by the given curves about the line y = 5. y = 5x , y = 5sqrt(x) find the volume

  • This Question is Closed
  1. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    noooooooo!!!!!!!!!!......well.......maybe ;)

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

    ;) helloo life saver xD

  3. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the interval is x=[0,1] again

  4. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    pi {S} [5x-5]^2 - [5sqrt(x)-5]^2 dx ; [0,1]

  5. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\pi \int\limits_{0}^{1} (25x^2 +25 -50x)-(25x +25 -50\sqrt(x)).dx\]

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

    the boundary wouldnt be from 0, 5 ? cuz it intersects at (1,5) i think

  7. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    5*5 = 25; 5*sqrt(5) != 25 :)

  8. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    5*1 = 5 ; 5*sqrt(1) = 5

  9. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the x interval is from 0 to 1; th ey interval would be from 0 to 5

  10. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but we only need use one interval

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

    ohh 5 is the y interval. oops lol ><

  12. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    http://www.wolframalpha.com/input/?i=pi+*+int%28+ [5x-5]^2+-+[5sqrt%28x%29-5]^2%29+dx++from+0+to+1

  13. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well that cut short lol

  14. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    copy paste that whole thing itno your address bar to see the results

  15. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    π ∫ (25x2−75x+50√x) dx is what the integral simplifies to before integrating

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

    got it :) i have one quick question. when youre given a line to rotate around, like lets say y = 1, and youre given two equations

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

    you would plug in 1 for y, and move everything to one side right?

  18. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1 for y?

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

    like you know how for this prob, we were told to rotate the region about the line y = 5 right

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

    so you simply plugged in 5 for y into both the equations

  21. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes; so subtract 5 from the functions to get it to the 0 line

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

    and moved everything onto one side ?

  23. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    y= 5x -5 y = 5sqrt(x) -5

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

    gotcha. and you would do the same if we were told to rotate around the line lets say for example, x = 4 right?

  25. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if it were x = 4; we would most likely modify the equations to satiisfy a y variable and subtrat 4 from them

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

    ooh okay, i understand now :) sorry i have another question xD when it says to rotate around lets say the y or x axis, how would you go about solving for that type of question?

  27. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    weve been focusing on disk methods; but the shell method is just a good for volume of rotation

  28. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    when we rotate around y; have your equations and interval ready for 'x' when we rotate around x; just have the equations and interal in terms of 'y'

  29. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the shell method is pretty cool to imagine; we take areas of flattened tin cans and add them up :)

  30. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    imagine a tin can; it has a height of" f(x) when we cut it up the side and spread it out we have the area of a flat rectangular sheet right?

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

    correct

  32. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the width of this sheet is the circumference of the bottom circle; 2pi [x]

  33. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the area of the sheet is widht * height: 2pi x[f(x)]

  34. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    add up all the sheets to get the area of the solid...volume of the solid that is

  35. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it cleans up the integral alot when youcan do it

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

    ooh. i should practice the shell method xD im so used to squaring the big R and little r for these volume type of problems lol i have one last exam tomorrow and a final next week for calculus. wish me luck ! hehe xD

  37. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Gluck :)

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

    thank you :D and thank you for all your help, i truly appreciate it :')

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

    *off to study i go* ;)

  40. 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.