Find the area inside the loop of the following limacon: r = 7 − 14 sin (θ). Please help!
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Originally Posted by Del Find the area inside the loop of the following limacon: r = 7 − 14 sin (θ). Please help! to find the limits of integration we set r =0 so we get After integrating I get
Originally Posted by Del Find the area inside the loop of the following limacon: r = 7 − 14 sin (θ). Please help! did you draw the graph? now that we have drawn it, we see that the inner loop happens when the graph goes to the origin, that is, when . so let's solve for that: for thus, the area is given by: EDIT: Geez, too late. Thanks a lot EmptySet!
We can factor out the 7 and write it as Then, we get Oops, beat to the punch. At least we agree.
Originally Posted by galactus EDIT ... Well, we agree. That's good. Yes, the one benefit to posting after others have posted.
I didn't just copy what you all did. What would be the point in that. I was in the middle of it when you fellas posted.
Originally Posted by galactus I didn't just copy what you all did. What would be the point in that. I was in the middle of it when you fellas posted. of course not. no one suggested that. but it's good that we all agree. our answers confirm one another. i mean, what are the chances we all got it wrong ...
I'm sorry, I misunderstood what you meant.
Originally Posted by galactus I'm sorry, I misunderstood what you meant. that's alright. no hard feelings whatsoever
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