2019 AP Calculus AB FRQ #5

Let R be the region enclosed by the graphs of g(x) = −2 + 3 * cos( pi/2 * x) and h(x) = 6 - 2 * (x-1)^2, the y-axis, and the vertical line x = 2, as shown in the figure above.
(a) Find the area of R.
(b) Region R is the base of a solid. For the solid, at each x the cross section perpendicular to the x-axis has area A(x) = 1 / x + 3. Find the volume of the solid.
(c) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line y = 6.
Timestamps
Intro: 00:00
Part a: 00:16
Part b: 08:29
Part c: 10:49