oh i forgot to attach my drawing of the graph, here it is
Question: Given the two polar equations r=5-3cos(θ) and r=5-3sin(θ) find the area of the region common to both curves.
So using the equation A= 1/2∫ r^2 dθ, the limits of integration I get by equating the two equations are θ= π/4, 5π/4. My question is am i setting this up all right and my equation to find the area is A = ∫(5−3cos(θ))^2 dθ + ∫(5−2sin(θ))^2 dθ. Can someone let me know if this is correct or what I'm doing wrong please
so instead of what i had at the beginning (A = 1-2∫(5−3cos(θ))^2 dθ + ∫(5−2sin(θ))^2 dθ)
i can just take A = ∫(5−2sin(θ))^2)dθ)? and because it was multiplied by two it will give me the area of the yellow and blue area (graph)? would i still keep the same limits of integration?
okay so if i expand it out then i would get
(5-3sin(ɵ))(5-3sin(ɵ))
25-15sin(ɵ)-15sin(ɵ)-9sin^2(ɵ)
25+9sin^2(ɵ)
25+9(1/2-1/2cos(2ɵ)
25+9/2-9/2cos(2ɵ)
59/2-9/2cos(2ɵ)
okay so this is what i have so far, is there any mistakes or more simplifying i can do before i go ahead and integrate?