 14.2.6E: Given a vector field F and a closed smooth oriented curve C, what i...
 14.2.12E: Scalar line integrals with arc length as parameter Evaluate the fol...
 14.2.13E: Scalar line integrals with arc length as parameter Evaluate the fol...
 14.2.11E: Scalar line integrals with arc length as parameter Evaluate the fol...
 14.2.27E: Scalar line integrals in R3 Convert the line integral to an ordina...
 14.2.8E: Given a twodimensional vector field F and a smooth oriented curve ...
 14.2.10E: Sketch the oriented quarter circle from (1, 0) to (0, 1) and supply...
 14.2.29E: Scalar line integrals in R3 Convert the line integral to an ordina...
 14.2.45E: Work integrals in R3 Given the force field F, find the work require...
 14.2.63E: Mass and density A thin wire represented by the smooth curve C with...
 14.2.1E: How does a line integral differ from the singlevariable integral ?...
 14.2.2E: How do you evaluate the line integral ?cf ds, where C is parameter...
 14.2.3E: If a curve C is given by r(t) = ?t, t2?, what is r'(t) ?
 14.2.4E: Given a vector field F and a parameterized curve C, explain how to ...
 14.2.5E: How can ?c F. T ds be written in the alternative form
 14.2.15E: Scalar line integrals in the planea. Find a parametric description ...
 14.2.16E: Scalar line integrals in the planea. Find a parametric description ...
 14.2.17E: Scalar line integrals in the planea. Find a parametric description ...
 14.2.28E: Scalar line integrals in R3 Convert the line integral to an ordina...
 14.2.18E: Scalar line integrals in the planea. Find a parametric description ...
 14.2.19E: Scalar line integrals in the planea. Find a parametric description ...
 14.2.20E: Scalar line integrals in the planea. Find a parametric description ...
 14.2.21E: Average values Find the average value of the following functions on...
 14.2.22E: Average values Find the average value of the following functions on...
 14.2.24E: Average values Find the average value of the following functions on...
 14.2.46E: Work integrals in R3 Given the force field F, find the work require...
 14.2.23E: Average values Find the average value of the following functions on...
 14.2.64E: Heat flux in a plate A square plate R = {(x, y): 0 ? x ? 1, 0 ? y ?...
 14.2.25E: Scalar line integrals in R3 Convert the line integral to an ordina...
 14.2.26E: Scalar line integrals in R3 Convert the line integral to an ordina...
 14.2.30E: Scalar line integrals in R3 Convert the line integral to an ordina...
 14.2.31E: Length of curves Use a scalar line integral to find the length of t...
 14.2.32E: Length of curves Use a scalar line integral to find the length of t...
 14.2.33E: Line integrals of vector fields in the plane Given the following v...
 14.2.34E: Line integrals of vector fields in the plane Given the following v...
 14.2.35E: Line integrals of vector fields in the plane Given the following v...
 14.2.36E: Line integrals of vector fields in the plane Given the following ve...
 14.2.37E: Line integrals of vector fields in the plane Given the following v...
 14.2.38E: Line integrals of vector fields in the plane Given the following v...
 14.2.39E: Work integrals Given the force field F, find the work required to m...
 14.2.40E: Work integrals Given the force field F, find the work required to m...
 14.2.41E: Work integrals Given the force field F, find the work required to m...
 14.2.42E: Work integrals Given the force field F, find the work required to m...
 14.2.43E: Work integrals in R3 Given the force field F, find the work require...
 14.2.44E: Work integrals in R3 Given the force field F, find the work require...
 14.2.48E: Circulation Consider the following vector fields F and closed orien...
 14.2.49E: Flux Consider the vector fields and curves in Exercises 47?48.Circu...
 14.2.50E: Flux Consider the vector fields and curves in Exercises 47?48.Circu...
 14.2.51E: Explain why or why not Determine whether the following statements ...
 14.2.52E: Flying into a headwind An airplane flies in the xzplane, where x i...
 14.2.53E: Flying into a headwind a. How does the result of Exercise 52 change...
 14.2.54E: Changing orientation Let f(x, y) = x + 2y and let C be the unit cir...
 14.2.55E: Changing orientation Let f(x, y) = x and let C be the segment of th...
 14.2.56E: Zero circulation fields For what values of b and c does the vector ...
 14.2.57E: Zero circulation fieldsConsider the vector field F = ?ax + by, cx +...
 14.2.58E: Zero flux fieldsFor what values of a and d does the vector field F ...
 14.2.59E: Zero flux fieldsConsider the vector field F = ?ax + by, cx + dy?. S...
 14.2.60E: Work in a rotation field Consider the rotation field F = ? ?y, x? a...
 14.2.61E: Work in a hyperbolic field Consider the hyperbolic force field F = ...
 14.2.62E: Mass and density A thin wire represented by the smooth curve C with...
 14.2.66E: Flux across curves in a vector field Consider the vector field F = ...
 14.2.67AE: Looking ahead: Area from line integrals The area of a region R in t...
 14.2.68AE: Looking ahead: Area from line integrals The area of a region R in t...
 14.2.65E: Inverse force fields Consider the radial field , where p > 1 (the i...
 14.2.9E: How do you calculate the flux of a twodimensional vector field acr...
 14.2.14E: Scalar line integrals with arc length as parameter Evaluate the fol...
 14.2.47E: Circulation Consider the following vector fields F and closed orien...
 14.2.7E: How is the circulation of a vector field on a closed smooth oriente...
Solutions for Chapter 14.2: Calculus: Early Transcendentals 1st Edition
Full solutions for Calculus: Early Transcendentals  1st Edition
ISBN: 9780321570567
Solutions for Chapter 14.2
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 14.2 includes 68 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since 68 problems in chapter 14.2 have been answered, more than 139501 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.

Bias
A flaw in the design of a sampling process that systematically causes the sample to differ from the population with respect to the statistic being measured. Undercoverage bias results when the sample systematically excludes one or more segments of the population. Voluntary response bias results when a sample consists only of those who volunteer their responses. Response bias results when the sampling design intentionally or unintentionally influences the responses

Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S

Coordinate plane
See Cartesian coordinate system.

Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Geometric series
A series whose terms form a geometric sequence.

Law of sines
sin A a = sin B b = sin C c

Lemniscate
A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

Matrix element
Any of the real numbers in a matrix

Modified boxplot
A boxplot with the outliers removed.

Multiplication principle of counting
A principle used to find the number of ways an event can occur.

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Spiral of Archimedes
The graph of the polar curve.

Sum of an infinite series
See Convergence of a series

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.