Question

Evaluate the double intergal between the two cirlces

Answer 1

3down votefavoriteFind the area between the circles x2+y2=4x2+y2=4 and x2+y2=6xx2+y2=6x using polar coordinates.I have found that the equation of the first circle, call it C1C1, is r=2r=2 on the other hand, for C2C2, I get that its equation is r=6cosθr=6cosθ. Then, to find the bounds of integration, I have found that their angle of intersection should be θ=arccos(1/3)θ=arccos⁡(1/3) and θ=−arccos(1/3)θ=−arccos⁡(1/3). Then, to set up the double integral:A=∫arccos(1/3)−arccos(1/3)∫26cosθrdrdθA=∫−arccos⁡(1/3)arccos⁡(1/3)∫6cos⁡θ2rdrdθHowever, when evaluating this integral with the calculator, I get a negative value. What would be the problem in this case? Thanks in advance for your help.