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anonymous

  • 4 years ago

Find the area of the region that lies inside both curves r = A*sin(theta) and r = B*sin(theta), A > 0, B > 0?

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  1. perl
    • 4 years ago
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    what does your notes say

  2. dumbcow
    • 4 years ago
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    these are polar equations?

  3. anonymous
    • 4 years ago
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    yes

  4. lgbasallote
    • 4 years ago
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    ...i am thinking...integration???

  5. anonymous
    • 4 years ago
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    yes

  6. lgbasallote
    • 4 years ago
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    i hate integration -____- we haven't taken that lesson yet. Sorry. Can't help :))

  7. perl
    • 4 years ago
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    when does A sin t = B sin t

  8. dumbcow
    • 4 years ago
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    well with rectangular coordinates, you just integrate f(x) -g(x) from where they intersect does it apply with polar coordinates as well? not as familiar working with polar :|

  9. perl
    • 4 years ago
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    nope

  10. perl
    • 4 years ago
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    cool picture

  11. perl
    • 4 years ago
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    thats very creative :)

  12. dumbcow
    • 4 years ago
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    haha thanks

  13. perl
    • 4 years ago
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    try an example,

  14. perl
    • 4 years ago
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    r = sin theta, r = 2 sin theta

  15. perl
    • 4 years ago
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    here is Paul's notes http://tutorial.math.lamar.edu/Classes/CalcII/PolarArea.aspx

  16. dumbcow
    • 4 years ago
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    wait they would never intersect right?

  17. perl
    • 4 years ago
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    they should

  18. dumbcow
    • 4 years ago
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    ha except at theta = npi

  19. perl
    • 4 years ago
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    integral 1/2 (r1^2 - r2^2 )

  20. perl
    • 4 years ago
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    where r = f(theta)

  21. perl
    • 4 years ago
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    ok so i graphed r = sin theta, and r= |dw:1328796260702:dw|2 sin theta

  22. perl
    • 4 years ago
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    and sin theta = 2 sin theta when theta = 0, 2pi

  23. perl
    • 4 years ago
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    so in your problem , we can assume without loss of generality, A > B. in which case we have |dw:1328796488104:dw|

  24. perl
    • 4 years ago
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    |dw:1328796701325:dw|

  25. perl
    • 4 years ago
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    |dw:1328796760182:dw|

  26. perl
    • 4 years ago
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    you can even make it less restrictive by saying |dw:1328799289713:dw|

  27. nikvist
    • 4 years ago
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    http://openstudy.com/users/nikvist#/updates/4f334085e4b0fc0c1a0b763d

  28. perl
    • 4 years ago
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    did you test your solution?

  29. perl
    • 4 years ago
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    your solution does not work for r = 2 sin theta, r = 1 sin theta

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