Find the area of the region that lies inside both curves. r = 3 + cosθ , r = 3 + 2sinθ

Question

please help with this Ive been trying to do this question for hours and I don't understand.

Answer 1

First of all, you need to know whether you want the algebraic area of the actual physical area.

Then plot the 2 curves (e.g. use DESMOS) which will show 2 points of intersection on the line y=.5x.

The curves intersect when θ=approximately 26.6 degrees and degrees and θ=approximately 206.6 degrees (obtained by setting the 2 equations equal to each other and solving for θ) You will need to obtain the area of each of 4 regions separately by integration using the integration formula for polar co-ordinates and radian measure.

The negative area of the cardioid is between 206.6 degrees and 360 and the positive area in between 360 and 386.6 degrees.

MY BAD on remembering that arctan .5 is NOT 30 degrees!.