Find the area of the region that lies inside both r^(2) = 2sin(2(theta)) and r =

Question

Find the area of the region that lies inside both r^(2) = 2sin(2(theta)) and r = 1

Area:???

Right answer= 5 stars

wrong answer = 1 star

Explanation / Answer

let they be curve 1 and curve2 respectively the two curves will intersect at theta=15 and 75 degrees now if draw the graph of both of them from theta = 15 to theta = 75 circle , the curve 1 will have more radius than curve 2 as asked we need to find the area that lies in both of them. => total area= 2(area of curve 1 under limits 0 to 15 degrees +area of curve 2 wth origin under limits 15 to 75 degrees +area of curve 1 under limits 75 to 90 degrees) [we need to observe that theta range is b/w 0 and 90 degrees or from 180 to 270 degrees for r^2 to be positive as it is symmetric in both ranges we multiply the area in one range with 2 to get the total area so total area = 2(integral of 2sin2theta under limits 0 to 15 degrees+ntegral of 2sin2theta under limits 75 to 90 degrees+integral of 1 under limits 15 to 75 degrees) =2.[1-(root3)/2]+[1-(root3)/2]+[60degrees] (repectively) =2.63 units approx

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