I have posted a picture to show the work.
I had help. I understand that we need to subtract off the one function from another, like how integrals are to get the a specific area. Just not sure how to do that.
I know to find the intersection points on any graph you set the two functions equal to each other, here I did that and got 1/2 = cos(θ), where that is true is at θ = 1/2 and θ = 5π/3. So those are the two intersecting points, but I don't understand how this helps to isolate the area of the curve r = 1 while removing the portion that r = 2cos(θ) is overlapping.
And integral follows that I don't understand.
How do we know which function to have in the first integral and which function to have in the second?
Also, how do we know to set the limits of integration for the first one to be: π/3 to 5π/3 and then have the second from π/3 to 2π/3?
Thank you
Answers & Comments
Verified answer
The graph of r = 1 is a circle , a center at the origin and the radius is 1. The graph of r = 2 cos theta is a circle of radius 1,a center at ( 1, 0 ). You can make a table with the angles theta from 0 to 2 pi, then find the corresponding values of r. The intersection ponts are theta equal pi/3 and 5pi/3. A = 1/2 int from pi/3 to pi/2 of ( 1 = 2cos theta ) d( theta) + 1/2 int from pi/2 to pi of [ 1 d( theta )]. Finally, multiplying by 2.