Problem 1E: CONCEPT CHECK Line integral What is the physical significance of each line integral? a) C1ds b)... Problem 2E: CONCEPT CHECK Orientation of a Curve Describe how reversing the orientation of the curve C affects... Problem 3E: Finding a Piecewise Smooth Parametrization In Exercises 38, find a piecewise smooth parametrization... Problem 4E Problem 5E: Finding a Piecewise Smooth Parametrization In Exercises 38, find a piecewise smooth parametrization... Problem 6E: Finding a Piecewise Smooth Parametrization In Exercises 38, find a piecewise smooth parametrization... Problem 7E: Finding a Piecewise Smooth Parametrization In Exercises 38, find a piecewise smooth parametrization... Problem 8E: Finding a Piecewise Smooth Parametrization In Exercises 38, 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: Evaluating a Line Integral In Exercises 9-12, (a) find a parametrization of the path C , and (b)... Problem 12E: Evaluating a Line Integral In Exercises 9-12, (a) find a parametrization of the path C, and (b)... Problem 13E: Evaluating a Line Integral In Exercises 1316, (a) find a piecewise smooth parametrization of the... Problem 14E Problem 15E: Evaluating a Line Integral In Exercises 1316, (a) find a piecewise smooth parametrization of the... Problem 16E: Evaluating a Line Integral In Exercises 1316, (a) find a piecewise smooth parametrization of the... Problem 17E: Evaluating a Line Integral In Exercises 17 and 18, (a) find a piecewise smooth parametrization of... Problem 18E: Evaluating a Line Integral In Exercises 17 and 18, (a) find a piecewise smooth parametrization of... 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: Mass In Exercises 23 and 24, find the total mass of a spring with density in the shape of the... Problem 24E: Mass In Exercises 23 and 24, find the total mass of a spring with density in the shape of the... Problem 25E: Mass In Exercises 25-28, find the total mass of the wire with density whose shape is modeled by r.... 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 Problem 31E Problem 32E: Evaluating a Line Integral of a Vector Field In Exercises 29-34, evaluate cFdr.... Problem 33E: Evaluating a Line Integral of a Vector Field In Exercises 29-34, evaluate cFdr.... Problem 34E Problem 35E: Evaluating a Line Integral of a Vector Field Using Technology In Exercises 35 and 36, use a computer... Problem 36E Problem 37E: Work In Exercises 37-42, find the work done by the force field F on a particle moving along the... Problem 38E: Work In Exercises 37-42, find the work done by the force field F on a particle moving along the... Problem 39E: Work In Exercises 37-42, find the work done by the force field F on a particle moving along the... Problem 40E: Work In Exercises 3742, find the work done by the force field F on a particle moving along the given... Problem 41E Problem 42E: Work In Exercises 3742, find the work done by the force field F on a particle moving along the given... Problem 43E: Work In Exercises 43-46, determine whether the work done along the path C is positive, negative, or... Problem 44E: Work In Exercises 43-46, determine whether the work done along the path C is positive, negative, or... Problem 45E: Work In Exercises 43-46, determine whether the work done along the path C is positive, negative, or... Problem 46E: Work In Exercises 43-46, determine whether the work done along the path C is positive, negative, or... Problem 47E: Evaluating a Line Integral of a Vector Field In Exercises 47 and 48, evaluate CFdr for each curve.... 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: Evaluating a Line Integral in Differential Form In Exercises 53-56, evaluate the line integral along... Problem 57E: Evaluating a Line Integral in Differential Form In Exercises 5764, evaluate C(2xy)dx+(x+3y)dy. C: x... Problem 58E: Evaluating a Line Integral in Differential Form In Exercises 5764, evaluate C(2xy)dx+(x+3y)dy. C:... Problem 59E: Evaluating a Line Integral in Differential Form In Exercises 5764, evaluate C(2xy)dx+(x+3y)dy. C:... Problem 60E: Evaluating a Line Integral in Differential Form In Exercises 5764, evaluate C(2xy)dx+(x+3y)dy. C:... Problem 61E: Evaluating a Line Integral in Differential Form In Exercises 5764, evaluate C(2xy)dx+(x+3y)dy. C:... Problem 62E Problem 63E Problem 64E Problem 65E: Lateral Surface Area In Exercises 65-72, find the area of the lateral surface (see figure) over the... Problem 66E Problem 67E: Lateral Surface Area In Exercises 65-72, find the area of the lateral surface (see figure) over the... Problem 68E: Lateral Surface Area In Exercises 65-72, find the area of the lateral surface (see figure) over the... Problem 69E Problem 70E Problem 71E Problem 72E: Lateral Surface Area In Exercises 65-72, find the area of the lateral surface (see figure) over the... Problem 73E Problem 74E Problem 75E Problem 76E Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E Problem 82E: Line Integrals Let F(x,y)=2xi+xy2j and consider the curve y=x2 from (0,0) to (2,4) in the xy-plane.... Problem 83E Problem 84E: HOW DO YOU SEE IT? For each of the following, determine whether the work done in moving an object... Problem 85E: True or False? In Exercises 85 and 86, determine whether the statement is true or false. If it is... Problem 86E: True or False? In Exercises 85 and 86, determine whether the statement is true or false. If it is... Problem 87E format_list_bulleted