Problem 1E: In Exercises 1–12, sketch the region described by the following cylindrical coordinates in... Problem 2E: In Exercises 1–12, sketch the region described by the following cylindrical coordinates in... Problem 3E: In Exercises 1–12, sketch the region described by the following cylindrical coordinates in... Problem 4E: In Exercises 1–12, sketch the region described by the following cylindrical coordinates in... Problem 5E: In Exercises 1–12, sketch the region described by the following cylindrical coordinates in... Problem 6E Problem 7E: In Exercises 1–12, sketch the region described by the following cylindrical coordinates in... Problem 8E: In Exercises 1–12, sketch the region described by the following cylindrical coordinates in... Problem 9E: In Exercises 1–12, sketch the region described by the following cylindrical coordinates in... Problem 10E Problem 11E: In Exercises 1–12, sketch the region described by the following cylindrical coordinates in... Problem 12E Problem 13E: In Exercises 13−22, sketch the region described by the following spherical coordinates in... Problem 14E: In Exercises 13−22, sketch the region described by the following spherical coordinates in... Problem 15E: In Exercises 13−22, sketch the region described by the following spherical coordinates in... Problem 16E Problem 17E: In Exercises 13−22, sketch the region described by the following spherical coordinates in... Problem 18E Problem 19E Problem 20E: In Exercises 13−22, sketch the region described by the following spherical coordinates in... Problem 21E: In Exercises 13−22, sketch the region described by the following spherical coordinates in... Problem 22E Problem 23E: Evaluate the cylindrical coordinate integrals in Exercises 23-28. 23. 0201r2r2rdzdrd Problem 24E: Evaluate the cylindrical coordinate integrals in Exercises 23−28.
24.
Problem 25E: Evaluate the cylindrical coordinate integrals in Exercises 23-28. 25. 020/203+24r2rdzdrd Problem 26E Problem 27E: Evaluate the cylindrical coordinate integrals in Exercises 23–28.
27.
Problem 28E Problem 29E: The integrals we have seen so far suggest that there are preferred orders of integration for... Problem 30E Problem 31E Problem 32E Problem 33E: Let D be the region bounded below by the plane z = 0, above by the sphere x2 + y2 + z2 = 4, and on... Problem 34E: Let D be the region bounded below by the cone and above by the paraboloid . Set up the triple... Problem 35E: Give the limits of integration for evaluating the integral Df(r,,z)rdzdrd as an iterated integral... Problem 36E: Convert the integral
to an equivalent integral in cylindrical coordinates and evaluate the result.
Problem 37E: In Exercises 37–42, set up the iterated integral for evaluating over the given region D.
37. D is... Problem 38E: In Exercises 37–42, set up the iterated integral for evaluating over the given region D.
38. D is... Problem 39E: In Exercises 37–42, set up the iterated integral for evaluating over the given region D.
39. D is... Problem 40E: In Exercises 37–42, set up the iterated integral for evaluating over the given region D.
40. D is... Problem 41E: In Exercises 37–42, set up the iterated integral for evaluating over the given region D.
41. D is... Problem 42E Problem 43E: Evaluate the spherical coordinate integrals in Exercises 43–48.
43.
Problem 44E: Evaluate the spherical coordinate integrals in Exercises 4348. 44. 020/402(cos)2sinddd Problem 45E: Evaluate the spherical coordinate integrals in Exercises 43–48.
45.
Problem 46E Problem 47E: Evaluate the spherical coordinate integrals in Exercises 43–48.
47.
Problem 48E Problem 49E: The previous integrals suggest there are preferred orders of integration for spherical coordinates,... Problem 50E: The previous integrals suggest there are preferred orders of integration for spherical coordinates,... Problem 51E: The previous integrals suggest there are preferred orders of integration for spherical coordinates,... Problem 52E Problem 53E: Let D be the region in Exercise 33. Set up the triple integrals in spherical coordinates that give... Problem 54E: Let D be the region bounded below by the cone and above by the plane z = 1. Set up the triple... Problem 55E: In Exercises 55–60, (a) find the spherical coordinate limits for the integral that calculates the... Problem 56E: In Exercises 55–60, (a) find the spherical coordinate limits for the integral that calculates the... Problem 57E: In Exercises 55–60, (a) find the spherical coordinate limits for the integral that calculates the... Problem 58E Problem 59E: In Exercises 55–60, (a) find the spherical coordinate limits for the integral that calculates the... Problem 60E: In Exercises 55–60, (a) find the spherical coordinate limits for the integral that calculates the... Problem 61E: Set up triple integrals for the volume of the sphere ρ = 2 in (a) spherical, (b) cylindrical, and... Problem 62E Problem 63E: Let D be the smaller cap cut from a solid ball of radius 2 units by a plane 1 unit from the center... Problem 64E Problem 65E: Find the volumes of the solids in Exercises 65–70.
Problem 66E: Find the volumes of the solids in Exercises 65–70.
Problem 67E: Find the volumes of the solids in Exercises 65–70.
Problem 68E Problem 69E: Find the volumes of the solids in Exercises 65–70.
69.
Problem 70E Problem 71E: Sphere and cones Find the volume of the portion of the solid sphere that lies between the cones ... Problem 72E Problem 73E Problem 74E Problem 75E: Cylinder and paraboloid Find the volume of the region bounded below by the plane z = 0, laterally by... Problem 76E: Cylinder and paraboloids Find the volume of the region bounded below by the paraboloid z = x2+ y2,... Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E: Region trapped by paraboloids Find the volume of the region bounded above by the paraboloid z = 5 –... Problem 82E: Paraboloid and cylinder Find the volume of the region bounded above by the paraboloid z = 9 – x2 –... Problem 83E Problem 84E Problem 85E Problem 86E Problem 87E: Find the average value of the function f(, , ) = over the solid ball 1. Problem 88E: Find the average value of the function f(ρ, ϕ, θ) = ρ cos ϕ over the solid upper ball ρ ≤ 1, 0 ≤ ϕ ≤... Problem 89E Problem 90E Problem 91E Problem 92E Problem 93E Problem 94E Problem 95E Problem 96E Problem 97E Problem 98E Problem 99E: Variable density A solid is bounded below by the cone and above by the plane z = 1. Find the center... Problem 100E: Variable density A solid ball is bounded by the sphere ρ = a. Find the moment of inertia about the... Problem 101E Problem 102E Problem 103E Problem 104E: Mass of planet’s atmosphere A spherical planet of radius R has an atmosphere whose density is ,... format_list_bulleted