Which of the following represents the area of the shaded region in the figure above? ∫dcf(y)dy
the integral from c to d of f y d y
A

∫ba(d−f(x))dx
the integral from A to b of open paren d minus f of x close paren, dx
B

f′(b)−f′(a)
f prime times b minus f prime times A
C

(b−a)[f(b)−f(a)]
open paren b minus A close paren times open bracket f of b minus f of A close bracket
D

(d−c)[f(b)−f(a)]

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)