 18.1: The figures in Exercises 12 show a vector field F and a curveC. Dec...
 18.2: The figures in Exercises 12 show a vector field F and a curveC. Dec...
 18.3: For the vector fields in Exercises 34, is the line integral positiv...
 18.4: For the vector fields in Exercises 34, is the line integral positiv...
 18.5: Is C(3i + 4j ) dr , where C is the line from (5, 2) to(1, 8), a vec...
 18.6: Is C(xi + yj ) dr , where C is the line from (0, 2) to(0, 6), a vec...
 18.7: In Exercises 712, findC F dr for the given F and C.F = 6i 7j , and ...
 18.8: In Exercises 712, findC F dr for the given F and C.F = xi + yj and ...
 18.9: In Exercises 712, findC F dr for the given F and C.F = xi + yj and ...
 18.10: In Exercises 712, findC F dr for the given F and C.F = (x2 y)i + (y...
 18.11: In Exercises 712, findC F dr for the given F and C.F = xi + yj + zk...
 18.12: In Exercises 712, findC F dr for the given F and C.F = xyi +(xy)j a...
 18.13: In Exercises 1314, evaluate the line integrals..C 3x2dx+4ydy where ...
 18.14: In Exercises 1314, evaluate the line integrals.C ydx+xdy where C is...
 18.15: In Exercises 1521, which of the vector fields are pathindependenton...
 18.16: In Exercises 1521, which of the vector fields are pathindependenton...
 18.17: In Exercises 1521, which of the vector fields are pathindependenton...
 18.18: In Exercises 1521, which of the vector fields are pathindependenton...
 18.19: In Exercises 1521, which of the vector fields are pathindependenton...
 18.20: In Exercises 1521, which of the vector fields are pathindependenton...
 18.21: In Exercises 1521, which of the vector fields are pathindependenton...
 18.22: In Exercises 2227, find the line integral of F = 5xi + 3xjalong the...
 18.23: In Exercises 2227, find the line integral of F = 5xi + 3xjalong the...
 18.24: In Exercises 2227, find the line integral of F = 5xi + 3xjalong the...
 18.25: In Exercises 2227, find the line integral of F = 5xi + 3xjalong the...
 18.26: In Exercises 2227, find the line integral of F = 5xi + 3xjalong the...
 18.27: In Exercises 2227, find the line integral of F = 5xi + 3xjalong the...
 18.28: In Exercises 2830, find the line integral of F around C1 andC2, whe...
 18.29: In Exercises 2830, find the line integral of F around C1 andC2, whe...
 18.30: In Exercises 2830, find the line integral of F around C1 andC2, whe...
 18.31: Which two of the vector fields (i)(iv) could representgradient vec...
 18.32: Let F (x, y) be the pathindependent vector field in Figure18.57. T...
 18.33: If C is r = (cos t)i +(sin t)j for 0 t 2, we knowC F (r ) dr = 12. ...
 18.34: Let C be the straight path from (0, 0) to (5, 5) and letF = (y x + ...
 18.35: The line integral of F = (x + y)i + xj along each ofthe following p...
 18.36: 3639 refer to the starshaped region R in Figure18.58.Let C be the ...
 18.37: 3639 refer to the starshaped region R in Figure18.58.Let C be the ...
 18.38: 3639 refer to the starshaped region R in Figure18.58.Let C be the ...
 18.39: 3639 refer to the starshaped region R in Figure18.58.Let C be the ...
 18.40: Let F = 2yi + 5xj . Let C be the Mshaped closedcurve consisting of...
 18.41: Let F = 2xeyi +x2eyj and G = (xy)i +(x+y)j .Let C be the path consi...
 18.42: Let F = (x2 + 3x2y4)i + 4x3y3j and G = (x4 +x3y2)i + x2y3j . Let C1...
 18.43: Calculate the line integral of F = yi + xj along thefollowing paths...
 18.44: Let C1 and C2 be the curves in Figure 18.59. Let F =(6x + y2)i + 2x...
 18.45: Let F = xi + yj . Find the line integral of F :(a) Along the xaxis...
 18.46: (a) Sketch the curves C1 and C2:C1 is (x, y) = (0, t) for 1 t 1C2 i...
 18.47: Draw an oriented curve C and a vector field F alongC that is not al...
 18.48: (a) Sketch the curve, C, consisting of three parts, C =C1 + C2 + C3...
 18.49: For each of the following vector fields in the plane, useGreens The...
 18.50: Suppose P and Q both lie on the same contour of f.What can you say ...
 18.51: Figure 18.61 shows level curves of the function f(x, y).(a) Sketch ...
 18.52: (a) ComputeC v dr where v = yi + 2xj and C is(i) The line joining (...
 18.53: Let C be the straight path from (0, 0) to (5, 5) and letF = (y x + ...
 18.54: Let F = F1i + F2j andF2x F1y = 3(x2 + y2) (x2 + y2)3/2.Let Ca be th...
 18.55: The fact that an electric current gives rise to a magneticfield is ...
 18.56: A central vector field is a vector field whose direction isalways t...
 18.57: free vortex circulating about the origin in the xyplane(or about th...
 18.58: Figure 18.64 shows the tangential velocity as a functionof radius f...
 18.59: Let Ca be the circle of radius a, centered at the origin,oriented i...
 18.60: If f is a potential function for the twodimensional vectorfield F ...
 18.61: Let F = (ax + by)i + (cx + dy)j . Evaluate the lineintegral of F al...
Solutions for Chapter 18: LINE INTEGRALS
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 18: LINE INTEGRALS
Get Full SolutionsSince 61 problems in chapter 18: LINE INTEGRALS have been answered, more than 44799 students have viewed full stepbystep solutions from this chapter. Chapter 18: LINE INTEGRALS includes 61 full stepbystep solutions. Calculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6.

De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

Degree
Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution

Difference of two vectors
<u1, u2>  <v1, v2> = <u1  v1, u2  v2> or <u1, u2, u3>  <v1, v2, v3> = <u1  v1, u2  v2, u3  v3>

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Halfplane
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

Implied domain
The domain of a function’s algebraic expression.

Inequality
A statement that compares two quantities using an inequality symbol

Leading term
See Polynomial function in x.

Mapping
A function viewed as a mapping of the elements of the domain onto the elements of the range

Matrix element
Any of the real numbers in a matrix

Negative linear correlation
See Linear correlation.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Polar axis
See Polar coordinate system.

Quadratic function
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

Seconddegree equation in two variables
Ax 2 + Bxy + Cy2 + Dx + Ey + F = 0, where A, B, and C are not all zero.

Slope
Ratio change in y/change in x

symmetric about the xaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Transformation
A function that maps real numbers to real numbers.

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.

zaxis
Usually the third dimension in Cartesian space.