The document contains instructions to find the volumes of solids generated by revolving regions bounded by graphs about axes. It gives the volume as 183.981 when revolving the region between the graphs y = 2x + 4 and y = ex about the x-axis. It also gives the volumes as 7/15 when revolving the region between y = x^2 + 1 and y = x + 1 about the x-axis and 4/5 when revolving the same region about the line y = -1.

2. Revolve about the x­axis
A(x) = tan2(x)
y = tan(x)
y = 0 x =
4
0.674 units

4. Find the volume of the solid generated by revolving about
the x­axis the region bounded by the line y = 2x + 4 and the
curve y = ex.

6. 183.981

7. The region bounded by the graph of y = x2 + 1 and the line
y = x + 1 generates various solids when rotated as follows:
a) about the x ­ axis b) about the line y = ­ 1

8. a) about the x ­ axis
7
15

9. b) about the line y = ­ 1
4
5

10. Exercise 8.2
Questions 11 ­ 19