Math 21D Homework
11th Edition Assignments

Solutions are provided by Dr. Kouba.

HW#1: Section 15.1 (pg 1063): # 1, 2, 4, 5, 7, 9-11, 13, 14, 16, (Setup but don't evaluate the integrals for the next 6 problems) 21, 23, 25, 26 (Change e^x to e^y), 28, 30, 31-33, 36, 38, (Setup both orders of integration but don't evaluate the integrals for the next 2 problems) 39, 40 ... Solutions

HW#2: Section 15.1 (pg 1063): # (Setup but don't evaluate integrals for the next 7 problems) 41, 43-47, 51, 54, 59, 61 ... Worksheet 1 ... Solutions

HW#3: Section 15.2 (pg 1073): # (Setup but don't evaluate integrals for the first 9 problems) (Setup integrals using both vertical and horizontal cross-sections for first 3 problems) 2, 3, 6, 7, 9, 11-14, 15a, 17 (Change region R to region bounded by:y=2x, y=0, x=2), 18 (Change function to 1/(x+1)y and change region R to region described by: 0 <= x <=1, e^x <= y <= e) ... Solutions

HW#4: Section 15.2 (pg 1073): # (Setup but don't evaluate integrals for the first 11 problems) 19, 21, 24, 26-28, 32-34, (Omit radius of gyration for problems 36 and 39) 36, 39, 41, 44, (For problems 53 and 54 use Pappus' Formula on page 1075 and assume that the density of the regions is the constant "delta" mass units over area units) 53, 54 ... Solutions

HW#5: Section 15.3 (pg 1081): # 1, 3, 4 (should be dx dy not dy dx), 6, 8, 9, 12, 13, 16, 18-20, (Setup but don't evaluate integrals for the next 5 problems) 22-25, 27, 29, 32, 33, 37a, 40, 42 ... Solutions

HW#6: Section 15.4 (pg 1090): # 7, 8, 11, 12, 16, 17, 19, 20, (Setup but don't evaluate integrals for the next 10 problems) 21, 23-25, 27, 29, 33, 34, 36, 38, 41, 42 ... Solutions

HW#7: Section 15.5 (pg 1096): # 2, 3 (Find the moment of inertia about a.) the x-axis and b.) the origin only.), 4a (Assume that the vertices are (0,0,0), (3,0,0), (0,2,0), and (0,0,1) and that the density at point (x,y,z) is xyz+1. Find the centroid and moment of inertia about the z-axiz only.), 5 (Assume that the density at point (x,y,z) is x+y+z+2. Find the moment of inertia about the y-axis and center of mass only.), 7a (Assume that the density at point (x,y,z) is e^-(x^2+y^2+z^2).), 11 (Assume that the density at point (x,y,z) is z/(x+y+2). Find the moment of inertia only), 13, 15abc (On part c. find the moment of inertia about the z-axis and the moment of inertia about the origin only.), 17, 26acd ... Solutions

HW#8: Section 15.6 (pg 1108): # 1, 6, 8, 10, (Setup but don't evaluate integrals for the next 15 problems) 11-13, 14 (Evaluate this one), 16, 18, 19, 43, 44, 47, 53, 56, 63, 68, 73 (Do moment of inertia only) ... Solutions

HW#9: Section 15.6 (pg 1108): # 21, 24, 26, 27, 30, (Setup but don't evaluate integrals for the next 18 problems. Use spherical coordinates on all problems except 41ab.) 31-35, 37, 38, 40ab, 41abc, 42b (Assume density at point P=(x,y,z) is z), 46, 52, 56, 65, 70 (Find x bar only) ... Solutions

HW#10: Section 15.7 (pg 1119): # 1, 4, 6, 8-10, 12, 14, 15a, 16, 20, 22 ... Solutions

HW#11: Section 13.1 (pg 900): # 1, 3, 4, 6, 8, 10, 12, 13, 15, 17, 19-21, 24, 26, 31, 33, 34, 36, 37de, 38, 40, 41, 43, 45, 48 ... Solutions

HW#12: Section 13.2 (pg 911): # 1-5, 7, 11, 13, 17, 18, 26, 28 ... Solutions

HW#13: Section 13.3 (pg 919): # 1, 3, 6, 7, 9, (For problems 12-14 write time t as a function of arc length s and write position vector function r bar as a a function of s.) 12-14, 17, 19, 20 ... Solutions

HW#14: Section 13.4 (pg 926): # 2-5, 9, 11, 13, 14, 17, 19, 21, 22 ... Solutions

HW#15: Section 16.1 (pg 1131): # 1-8, 10-13, 15-19, 22, 23, 24 (Find y bar only.), 25a , 27 (Omit radius of gyration.), 29 (Assume that density at point P=(x,y,z) is z+1. Find moment of inertia about the z-axis, moment of inertia about the origin, the z bar coordinate for center of mass, and the z bar coordinate for centroid.) ... Solutions

HW#16: Section 16.2 (pg 1142): # 1, 3-6, 7abc, 12abc, 13, 15, 17, 19-22, 31 (Do not plot horizontal and vertical components.), 32 (Do not plot horizontal and vertical components.), 35 ... Solutions

HW#17: Section 16.2 (pg 1142): # 23a, 24, 26, 27, 29ab, 30, 37, 40, 41, 43 ... Solutions

HW#18: Section 16.3 (pg 1152): # 1-10, 13, 14, 16, 17, 19, 20, 24, 25, 37 ... Solutions

HW#19: Section 16.4 (pg 1163): # 1, 2, 4, 5, 7, 8, 10-13, 15-20, 22, 24, 26, 29, 30, 33 ... Solutions

HW#20: Section 16.5 (pg 1174): # 1, 3, 5, 6, 7 (Assume that c=3.), 12, 13 (Assume that a=1.), 15, 17, 19-21, 24-27, 33 (Find x bar only. Find z bar first and use symmetry of region to conclude that x bar = y bar = z bar.), 35 (Find z bar only and the moment of inertia. Omit radius of gyration.) ... Solutions

HW#21: Section 16.6 (pg 1183): # 1, 4, 5, 7, 9, 11, 14a, 17, 20, 24, 27, 30, 34, 35, 37, 39, 40, 41 ... Solutions

HW#22: Section 16.7 (pg 1193): # 1, 3, 6, 7, 8, 13, 15, 17 ... Solutions

HW#23: Section 16.8 (pg 1204): # 5, 6c, 7, 8, 14, 16, 26 ... Solutions