The region R is bounded by the curves x = y² + 2, y = x - 4, and y = 0 (see figure).

a. Write a single integral that gives the area of R.

b. Write a single integral that gives the volume of the solid generated when R is revolved about the x-axis.

c. Write a single integral that gives the volume of the solid generated when R is revolved about the y-axis.

d. Suppose S is a solid whose base is R and whose cross sections perpendicular to R and parallel to the x-axis are semicircles. Write a single integral that gives the volume of S.

Transcribed Image Text:

УА x = y² + 2 х у 3х — 4 4 2.