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WA_1_Section_5.2_Calculus_Questions
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WA 1 Section 5.2 Calculus Questions
Section 5.2
2. Find the volume of the solid with cross-sectional area A(x). 0.01()10,010xAxex===
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 2120120xy=-for 120120x-==(units of feet). Find its volume.
12. A pottery jar has circular cross sections of radius 24sinx-inches for 02.xp== Sketch a picture of the jar and compute its volume.
18. Compute the volume of the solid formed by revolving the region bounded by 22,4yxyx==- about (a) the x-axis; (b) y = 4.
20. Compute the volume of the solid formed by revolving the region bounded by 2yx=and 2xy=about (a) the y-axis; (b) x = 1.
22. Compute the volume (exactly if possible and estimate if necessary) of the solid formed by revolving the region bounded by y= secx,
y= 0, x=4p- and x= 4p about (a) y = 2; (b) the x-axis.
WA 1, p. 1
26. Let R be the region bounded by 2yx=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 221xy+= is revolved about the y-axis. Show that the volume of the resulting solid is 43p.
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 ,,yxyx==-and 1,x= revolved about 1x=.
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 2yx=and 0,11yx=-==, 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 222xyy+=, revolved about y = 4.
12. Use cylindrical shells to compute the volume of the region bounded by 2xy=and x = 4, revolved about y = 2.
22. Use the best method available to find the volume of the region bounded by 22,(0)yxyxx=-=> and the y-axis revolved about (a) the x-axis, (b) the y-axis, (c) x =
WA 1, p. 2
–1, and (d) y = –1.
24. Use the best method available to find the volume of the region bounded by 1,2xyeyx=-=- 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 bysinyx=and 2yx=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. ln,13yxx===
10. Compute the arc length exactly.
y = 311,62xx+13x==
14. Compute the arc length exactly. 22ln(4),01yxx=-==
30. Set up the integral for the surface area of the surface of revolution, and approximate the integral with a numerical method. sin,0,yxxp=== revolved about the x-axis
WA 1, p. 3
32. Set up the integral for the surface area of the surface of revolution, and approximate the integral with a numerical method. 34,20,yxxx=--== 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. ,12,yxx=== revolved about the x-axis
WA 1, p. 4
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Calculus Homework Solutions
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