Name:
Name:
University ID:
Thomas Edison State University
Calculus II (MAT-232)
Section no.:
Semester and year:
Written Assignment 1
Answer all assigned exercises, and show all work. Each exercise is worth 5 points.
Section 5.2
2. Find the volume of the solid with cross-sectional area A(x).
6. Find the volume of a pyramid of height 160 feet that has a square base of side 300 feet. These dimensions are half those of the pyramid in example 2.1. How does the volume compare?
10. A dome “twice as big” as that of exercise 9 (see text) has outline for (units of feet). Find its volume.
12. A pottery jar has circular cross sections of radius inches for Sketch a picture of the jar and compute its volume.
18. Compute the volume of the solid formed by revolving the region bounded by about (a) the x-axis; (b) y = 4.
20. Compute the volume of the solid formed by revolving the region bounded by and about (a) the y-axis; (b) x = 1.
26. Let R be the region bounded by and y = 4. Compute the volume of the solid formed by revolving R about the given line.
(a) y = 4 (b) the y-axis (c) y = 6
(d) y = –2 (e) x = 2 (f) x = –4
32. Suppose that the circle is revolved about the y-axis. Show that the volume of the resulting solid is .
Section 5.3
4. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by and revolved about .
6. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by and , revolved about x = 2.
8. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and compute the volume for the region bounded by , revolved about y = 4.
12. Use cylindrical shells to compute the volume of the region bounded by and x = 4, revolved about y = 2.
22. Use the best method available to find the volume of the region bounded by and the y-axis revolved about (a) the x-axis, (b) the y-axis, (c) x = –1, and (d) y = –1.
24. Use the best method available to find the volume of the region bounded by and the x-axis revolved about the (a) x-axis and (b) y-axis.
26. Use the best method available to find the volume of the region bounded byand revolved about (a) y = 1, (b) x = 1, (c) the y-axis, and (d) the x-axis.
Section 5.4
4. Approximate the length of the curve using n secant lines for n = 2; n = 4.
14. Compute the arc length exactly.
30. Set up the integral for the surface area of the surface of revolution, and approximate the integral with a numerical method.
revolved about the x-axis
32. Set up the integral for the surface area of the surface of revolution, and approximate the integral with a numerical method.
revolved about the x-axis
36. Set up the integral for the surface area of the surface of revolution, and approximate the integral with a numerical method.
revolved about the x-axis
WA 1, p. 1
120120
x
-££
2
4sin
x
-
02.
x
p
££
22
,4
yxyx
==-
2
yx
=
2
xy
=
2
yx
=
22
1
xy
+=
4
3
p
,,
yxyx
==-
1,
x
=
1
x
=
2
yx
=
0,11
yx
=-££
22
2
xyy
+=
2
xy
=
2
2,(0)
yxyxx
=-=
1,2
x
yeyx
=-=-
sin
yx
=
2
yx
=
ln,13
yxx
=££
2
2ln(4),01
yxx
=-££
sin,0,
yxx
p
=££
3
4,20,
yxxx
=--££
,12,
yxx
=££
0.01
()10,010
x
Axex
=££
2
120
120
x
y
=-