anonymous
  • anonymous
find the area inside the cardioid r=1-sin theta and outside the circle r=1/2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
you just want an answer?
anonymous
  • anonymous
I would definitely exploit the symmetry so you only have one definite integral
anonymous
  • anonymous
i wanted to c how to do it

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anonymous
  • anonymous
the integral you want is\[\int^{\frac{3\pi}{2}}_{\frac{5\pi}{6}}\left[\left[1-\sin\theta\right]^2-1^2\right]d\theta\]
anonymous
  • anonymous
i am exploiting the symmetry
anonymous
  • anonymous
it is best to sketch the region for these problems
anonymous
  • anonymous
sorry that 1 should be 1/2
anonymous
  • anonymous
and one of your limits should be pi/6
anonymous
  • anonymous
well
anonymous
  • anonymous
what is the lower limit then?
anonymous
  • anonymous
its pi/6
anonymous
  • anonymous
what is you upper limit then?
anonymous
  • anonymous
5pi/6
anonymous
  • anonymous
are you looking at the graph of the region?
anonymous
  • anonymous
if you use those limits you will capture the wrong area
anonymous
  • anonymous
hey i figured it out ty
anonymous
  • anonymous
cool
anonymous
  • anonymous
those are tricky, the iterated integrals in multi-variable are even more awesome
anonymous
  • anonymous
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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