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anonymous

  • 5 years ago

find the area inside the cardioid r=1-sin theta and outside the circle r=1/2

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  1. anonymous
    • 5 years ago
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    you just want an answer?

  2. anonymous
    • 5 years ago
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    I would definitely exploit the symmetry so you only have one definite integral

  3. anonymous
    • 5 years ago
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    i wanted to c how to do it

  4. anonymous
    • 5 years ago
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    the integral you want is\[\int^{\frac{3\pi}{2}}_{\frac{5\pi}{6}}\left[\left[1-\sin\theta\right]^2-1^2\right]d\theta\]

  5. anonymous
    • 5 years ago
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    i am exploiting the symmetry

  6. anonymous
    • 5 years ago
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    it is best to sketch the region for these problems

  7. anonymous
    • 5 years ago
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    sorry that 1 should be 1/2

  8. anonymous
    • 5 years ago
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    and one of your limits should be pi/6

  9. anonymous
    • 5 years ago
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    well

  10. anonymous
    • 5 years ago
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    what is the lower limit then?

  11. anonymous
    • 5 years ago
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    its pi/6

  12. anonymous
    • 5 years ago
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    what is you upper limit then?

  13. anonymous
    • 5 years ago
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    5pi/6

  14. anonymous
    • 5 years ago
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    are you looking at the graph of the region?

  15. anonymous
    • 5 years ago
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    if you use those limits you will capture the wrong area

  16. anonymous
    • 5 years ago
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    hey i figured it out ty

  17. anonymous
    • 5 years ago
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    cool

  18. anonymous
    • 5 years ago
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    those are tricky, the iterated integrals in multi-variable are even more awesome

  19. anonymous
    • 5 years ago
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    yah. oh do you think you can help me with graphing a problem u can see the problem if u click on this link http://www.twiddla.com/511680

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spraguer (Moderator)
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