calculus question

Question

 

Find the area of the region that is inside the graph of r = 1 and outside of the graph of r = 1 + cos (θ).

	1.127
	1.215
	1.275
	1.375

I am getting 1.275, I'm not sure if that is right though.

Answer 1

If you graphed the two functions (use special values to get points), the intersection points are at π/2 and 3π/2.

The second function is inside the first between these two bounds but it is easier to use symmetry and take the integral from π/2 to π and double. Remember inner function< outer function within bounds of integration.

2∫[1-(1+cos θ)]dθ = 2∫-cos θ dθ = -2sin 0]_π/2^π = 2