AP Calculus BC: Question (1)
[image]

Let R be the shaded region bounded by the graphs of y =

and y =

and the vertical line x = 1, as shown in the figure above.

(a) Find the area of R.

- Find point of intersection:

(.238734, .488604)

- Find the Area

A = [image]

(b) Find the Volume of the solid generated when R is revolved about the horizontal line y = 1.

V = [image]

(c) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is a rectangle whose height is 5 times the length of its base in region R. Find the volume of this solid.

V = [image]