The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. the curves intersect at θ = π/3 and θ = 5π/3. (a) let r be the shaded region that is inside the graph of r = 4 and also outside the graph of r = 3 + 2cosθ, as shown in the figure above. write an expression involving an integral for the area of r. (b) find the slope of the line tangent to the graph of r = 3 + 2cosθ at θ = π/2. (c) a particle moves along the portion of the curve r = 3 + 2cosθ for 0 < θ < π/2. the particle moves in such a way that the distance between the particle and the origin increases at a constant rate of 3 units per second. find the rate at which the angle θ changes with respect to time at the instant when the position of the particle corresponds θ = π/3. indicate units of measure.