Please use this sheet and write or type answer under questions and leave space for comments from professor. Neat and legible showing all work.
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 =-