Question

Find the area of the inner loop of the limacon with polar equation r=3cosθ−2

theta 1= arccos(2/3) theta 2= -arccos(2/3)

i don't know why i'm getting the wrong answer. am i doing something wrong here?

Answer 1

this is what i'm doing. \[\int\limits_{\theta1}^{\theta2}\frac{ 1 }{ 2 }(3\cos(\theta)-2)^{2}\]
\[\frac{ 1 }{ 2 }\int\limits_{\theta1}^{\theta2}(9\cos^2(\theta)-12\cos(\theta)+4)\]
=\[\frac{ 17(\theta) }{ 4 }-\frac{ 9\sin(2\theta) }{ 8}-6\sin(theta)\]

plug in my theta's...and get the wrong answer....i really am starting to hate this.

Answer 2

@ganeshie8 can you help?

Answer 3

nvmd. i got it. had a + instead of a - sign