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

joannaj93 Group Title

Using a polar double integral, find the volume in the first octant below the surface z=xy, inside cylinder r=4cos(theta), and between the cylinders x^2 + y^2=4 and x^2 + y^2=8.

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1352751755636:dw|

    • 2 years ago
  2. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    in polar the three graphs are\[r=2\]\[r=2\sqrt2\]\[r=4\cos\theta\]can you find the intersection points in terms of theta?|dw:1352752221119:dw|

    • 2 years ago
  3. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    1st octant...

    • 2 years ago
  4. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Make the equations equal to one another...

    • 2 years ago
  5. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, and what do you get for theta?

    • 2 years ago
  6. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    arccos 2^(1/2)/2

    • 2 years ago
  7. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    well that's one, what angle does that correspond to? and what is the other intersection?

    • 2 years ago
  8. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    45 degrees

    • 2 years ago
  9. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    and 60 degrees

    • 2 years ago
  10. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, 45 and 60, but you better use radians in calc|dw:1352754013710:dw|

    • 2 years ago
  11. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1352754159926:dw|

    • 2 years ago
  12. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    so which fuunction is the outer radius and which one the inner radius for\[0\le\theta\le\frac\pi4\]?

    • 2 years ago
  13. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    r=2 is inner and r=2sqrt2 is outer...

    • 2 years ago
  14. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, good :) and for the interval\[\frac\pi4\le\theta\le\frac\pi3\]what is it?

    • 2 years ago
  15. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    r=4cos (theta) is outer and r=2sqrt2 is inner...

    • 2 years ago
  16. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I think you have the inner wrong|dw:1352754952806:dw|

    • 2 years ago
  17. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh, inner is r=2

    • 2 years ago
  18. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    right and what are your integrands?

    • 2 years ago
  19. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm not too sure about that

    • 2 years ago
  20. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    you are integrating xy sub in x=rcost, y=rsint

    • 2 years ago
  21. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    above t=theta in case you didn't guess also you need to use dA for polar coordinate

    • 2 years ago
  22. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so it'll be the double integral of r^2 cost sint...

    • 2 years ago
  23. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    that is the xy part, and what is dA in polar?

    • 2 years ago
  24. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    dr dt

    • 2 years ago
  25. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry, r dr dt

    • 2 years ago
  26. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, forget that extra r and you will be sorry :P so can you write your integrals yet?

    • 2 years ago
  27. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I dont think so

    • 2 years ago
  28. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    do you see that it will be two integrals?

    • 2 years ago
  29. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    im getting three rs and thethas

    • 2 years ago
  30. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    there are two regions to consider|dw:1352756391639:dw|what are the bounds for r and theta on the first integral? what are they on the second? those will be the bounds of your integral.

    • 2 years ago
  31. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    r=2 to 2√2 and t= 0 to pi/4 and r=2√2 to 4cosθ and t= 0 to pi/3

    • 2 years ago
  32. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    on the second region the lower bound on r is not 2√2 as we have already discussed, and the lower bound on theta is not 0, but the upper bound of the previous integral

    • 2 years ago
  33. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry about that. give me a sec

    • 2 years ago
  34. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    for the second integral: r=2 to 4cost and t= pi/4 to pi/3

    • 2 years ago
  35. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    good :) so how 'bout setting up those integrals? (two double intergals)

    • 2 years ago
  36. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits_{0}^{\pi/4}\int\limits\limits_{2}^{2\sqrt{2}}r ^{2}\cos \Theta \sin \Theta r dr d \Theta \]

    • 2 years ago
  37. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    that's the first one, yes

    • 2 years ago
  38. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits_{\pi/4}^{\pi/3} \int\limits_{2}^{4\cos \Theta} r2\cosΘ\sinΘrdrdΘ\]

    • 2 years ago
  39. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    yes, good :) then add them together to find the total voume happy integrating

    • 2 years ago
  40. joannaj93 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh, God this does not look like fun, but Thanks for the help :)

    • 2 years ago
  41. TuringTest Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    It's really not that hard if you can just remember to integrate with respect to theta and r separately, but I'm still too lazy to do it. Welcome!

    • 2 years 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.