1 Preparation For Calculus 2 Limits And Their Properties 3 Differentiation 4 Applications Of Differentiation 5 Integration 6 Differential Equations 7 Applications Of Integration 8 Integration Techniques And Improper Integrals 9 Infinite Series 10 Conics, Parametric Equations, And Polar Coordinates 11 Vectors And The Geometry Of Space 12 Vector-valued Functions 13 Functions Of Several Variables 14 Multiple Integration 15 Vector Analysis expand_more
15.1 Vector Fields 15.2 Line Integrals 15.3 Conservative Vector Fields And Independence Of Path 15.4 Green's Theorem 15.5 Parametric Surfaces 15.6 Surface Integrals 15.7 Divergence Theorem 15.8 Stokes's Theorem Chapter Questions expand_more
Problem 1E: CONCEPT CHECK Line integral What is the physical significance of each line integral? a) C1ds b)... Problem 2E Problem 3E: Finding a Piecewise Smooth Parametrization In Exercises 3-8, find a piecewise smooth parametrization... Problem 4E Problem 5E: Finding a Piecewise Smooth Parametrization In Exercises 3-8, find a piecewise smooth parametrization... Problem 6E Problem 7E: Finding a Piecewise Smooth Parametrization In Exercises 3-8, find a piecewise smooth parametrization... Problem 8E: Finding a Piecewise Smooth Parametrization In Exercises 3-8, find a piecewise smooth parametrization... Problem 9E: Evaluating a Line Integral In Exercises 9-12, (a) find a parametrization of the path C, and (b)... Problem 10E: Evaluating a Line Integral In Exercises 9-12, (a) find a parametrization of the path C, and (b)... Problem 11E Problem 12E Problem 13E Problem 14E: Evaluating a Line Integral In Exercises 13-16, (a) find a piecewise smooth parametrization of the... Problem 15E: Evaluating a Line Integral In Exercises 13-16, (a) find a piecewise smooth parametrization of the... Problem 16E: Evaluating a Line Integral In Exercises 13-16, (a) find a piecewise smooth parametrization of the... Problem 17E Problem 18E Problem 19E: Evaluating a Line Integral In Exercises 19-22, evaluate the line integral along the given path.... Problem 20E: Evaluating a Line Integral In Exercises 19-22, evaluate the line integral along the given path.... Problem 21E: Evaluating a Line Integral In Exercises 19-22, evaluate the line integral along the given path.... Problem 22E: Evaluating a Line Integral In Exercises 19-22, evaluate the line integral along the given path.... Problem 23E Problem 24E: Mass In Exercises 23 and 24, find the total mass of a spring with density in the shape of the... Problem 25E Problem 26E Problem 27E Problem 28E: Mass In Exercises 25-28, find the total mass of the wire with density whose shape is modeled by r.... Problem 29E: Evaluating a Line Integral of a Vector Field In Exercises 29-34, evaluate CFdr.... Problem 30E: Evaluating a Line Integral of a Vector Field In Exercises 29-34, evaluate CFdr.... Problem 31E Problem 32E Problem 33E Problem 34E: Evaluating a Line Integral of a Vector Field In Exercises 29-34, evaluate CFdr.... Problem 35E Problem 36E Problem 37E Problem 38E: Work In Exercises 37-42, find the work done by the force field F on a particle moving along the... Problem 39E Problem 40E: Work In Exercises 37-42, find the work done by the force field F on a particle moving along the... Problem 41E Problem 42E: Work In Exercises 37-42, find the work done by the force field F on a particle moving along the... Problem 43E: Work In Exercises 43-46, determine whether the work donealong the path is positive, negative, or... Problem 44E: Work In Exercises 43-46, determine whether the work done along the path is positive, negative, or... Problem 45E Problem 46E Problem 47E Problem 48E Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E: Evaluating a Line Integral in Differential Form In Exercises 53-56, evaluate the line integral along... Problem 54E Problem 55E Problem 56E Problem 57E: Evaluating a Line Integral in Differential Form In Exercises 57-64, evaluate C(2xy)dx+(x+3y)dy. C: x... Problem 58E: Evaluating a Line Integral in Differential Form In Exercises 57-64, evaluate C(2xy)dx+(x+3y)dy. C:... Problem 59E Problem 60E Problem 61E Problem 62E: Evaluating a Line Integral in Differential Form In Exercises 57-64, evaluate C(2xy)dx+(x+3y)dy. C:... Problem 63E Problem 64E Problem 65E Problem 66E: Lateral Surface Area In Exercises 65-72, find the area ofthe lateral surface (see figure) over the... Problem 67E Problem 68E Problem 69E Problem 70E: Lateral Surface Area In Exercises 65-72, find the area ofthe lateral surface (see figure) over the... Problem 71E Problem 72E: Lateral Surface Area In Exercises 65-72, find the area ofthe lateral surface (see figure) over the... Problem 73E Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E Problem 79E: Work Find the work done by a person weighing 175 pounds walking exactly one revolution up a circular... Problem 80E Problem 81E Problem 82E Problem 83E Problem 84E Problem 85E Problem 86E Problem 87E format_list_bulleted