Name: College ID: 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). A( x ) =10e0.01x , 0 x 10 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 y =120 - 120 x 120 (units of feet). Find its volume. x2 120 for x 12. A pottery jar has circular cross sections of radius 4 - sin 2 inches for 0 x 2p . Sketch a picture of the jar and compute its volume. 18. Compute the volume of the solid formed by revolving the region bounded by y =x 2 , y =4 - x 2 about (a) the x-axis; (b) y = 4. WA 1, p. 1 2 20. Compute the volume of the solid formed by revolving the region bounded by y =x and x = y 2 about (a) the y-axis; (b) x = 1. 2 26. Let R be the region bounded by y =x and y = 4. Compute the volume of the solid formed by revolving R about the given line. a) y = 4 (d) y = -2 (b) the y-axis (e) x = 2 (c) y = 6 (f) x = -4 2 2 32. Suppose that the circle x + y =1 is revolved about the y-axis. Show that the volume of 4 the resulting solid is 3 p . 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 y =x, y =- x, and x =1, revolved about x =1 . 6. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and 2 compute the volume for the region bounded by y =x and y =0, - 1 x 1 , revolved about x = 2. 8. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and 2 2 compute the volume for the region bounded by x +y =4 , revolved about y = 4. 2 12. Use cylindrical shells to compute the volume of the region bounded by x = y and x = 4, revolved about y = 2. 22. Use the best method available to find the volume of the region bounded by y =2 - x 2 , y = x ( x > 0) 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 y =e x - 1, y =2 - x 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 by y =sin x and y =x 2 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. y =ln x, 1 x 3 14. Compute the arc length exactly. y =2 ln(4 - x 2 ), 0 x 1 WA 1, p. 3 30. Set up the integral for the surface area of the surface of revolution, and approximate the integral with a numerical method. y =sin x, 0 x p , 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. y =x 3 - 4 x, - 2 x 0, 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. y = x , 1 x 2, revolved about the x-axis \f\f\f\f\f\f\f\f\f\f\f