 14.2.1: How does a line integral differ from the singlevariable integral 1...
 14.2.2: How do you evaluate the line integral 1C f ds, where C is parameter...
 14.2.3: If a curve C is given by r1t2 = 8t, t29, what is 0 r_1t2 0 ?
 14.2.4: Given a vector field F and a parameterized curve C, explain how to ...
 14.2.5: How can 1C F # T ds be written in the alternative form 1 b a 1 f 1t...
 14.2.6: Given a vector field F and a closed smooth oriented curve C, what i...
 14.2.7: How is the circulation of a vector field on a closed smooth oriente...
 14.2.8: Given a twodimensional vector field F and a smooth oriented curve ...
 14.2.9: How do you calculate the flux of a twodimensional vector field acr...
 14.2.10: Sketch the oriented quarter circle from 11, 02 to 10, 12 and supply...
 14.2.11: 1114. Scalar line integrals with arc length as parameter Evaluate t...
 14.2.12: 1114. Scalar line integrals with arc length as parameter Evaluate t...
 14.2.13: 1114. Scalar line integrals with arc length as parameter Evaluate t...
 14.2.14: 1114. Scalar line integrals with arc length as parameter Evaluate t...
 14.2.15: 1520. Scalar line integrals in the plane a. Find a parametric descr...
 14.2.16: 1520. Scalar line integrals in the plane a. Find a parametric descr...
 14.2.17: 1520. Scalar line integrals in the plane a. Find a parametric descr...
 14.2.18: 1520. Scalar line integrals in the plane a. Find a parametric descr...
 14.2.19: 1520. Scalar line integrals in the plane a. Find a parametric descr...
 14.2.20: 1520. Scalar line integrals in the plane a. Find a parametric descr...
 14.2.21: 2124. Average values Find the average value of the following functi...
 14.2.22: 2124. Average values Find the average value of the following functi...
 14.2.23: 2124. Average values Find the average value of the following functi...
 14.2.24: 2124. Average values Find the average value of the following functi...
 14.2.25: 2530. Scalar line integrals in 3 Convert the line integral to an or...
 14.2.26: 2530. Scalar line integrals in 3 Convert the line integral to an or...
 14.2.27: 2530. Scalar line integrals in 3 Convert the line integral to an or...
 14.2.28: 2530. Scalar line integrals in 3 Convert the line integral to an or...
 14.2.29: 2530. Scalar line integrals in 3 Convert the line integral to an or...
 14.2.30: 2530. Scalar line integrals in 3 Convert the line integral to an or...
 14.2.31: 3132. Length of curves Use a scalar line integral to find the lengt...
 14.2.32: 3132. Length of curves Use a scalar line integral to find the lengt...
 14.2.33: 3338. Line integrals of vector fields in the plane Given the follow...
 14.2.34: 3338. Line integrals of vector fields in the plane Given the follow...
 14.2.35: 3338. Line integrals of vector fields in the plane Given the follow...
 14.2.36: 3338. Line integrals of vector fields in the plane Given the follow...
 14.2.37: 3338. Line integrals of vector fields in the plane Given the follow...
 14.2.38: 3338. Line integrals of vector fields in the plane Given the follow...
 14.2.39: 3942. Work integrals Given the force field F, find the work require...
 14.2.40: 3942. Work integrals Given the force field F, find the work require...
 14.2.41: 3942. Work integrals Given the force field F, find the work require...
 14.2.42: 3942. Work integrals Given the force field F, find the work require...
 14.2.43: 4346. Work integrals in 3 Given the force field F, find the work re...
 14.2.44: 4346. Work integrals in 3 Given the force field F, find the work re...
 14.2.45: 4346. Work integrals in 3 Given the force field F, find the work re...
 14.2.46: 4346. Work integrals in 3 Given the force field F, find the work re...
 14.2.47: 4748. Circulation Consider the following vector fields F and closed...
 14.2.48: 4748. Circulation Consider the following vector fields F and closed...
 14.2.49: 4950. Flux Consider the vector fields and curves in Exercises 4748....
 14.2.50: 4950. Flux Consider the vector fields and curves in Exercises 4748....
 14.2.51: Explain why or why not Determine whether the following statements a...
 14.2.52: Flying into a headwind An airplane flies in the xzplane, where x i...
 14.2.53: Flying into a headwind a. How does the result of Exercise 52 change...
 14.2.54: Changing orientation Let f 1x, y2 = x + 2y and let C be the unit ci...
 14.2.55: Changing orientation Let f 1x, y2 = x and let C be the segment of t...
 14.2.56: For what values of b and c does the vector field F = 8by, cx9 have ...
 14.2.57: Consider the vector field F = 8ax + by, cx + dy9. Show that F has z...
 14.2.58: For what values of a and d does the vector field F = 8ax, dy9 have ...
 14.2.59: Consider the vector field F = 8ax + by, cx + dy9. Show that F has z...
 14.2.60: Work in a rotation field Consider the rotation field F = 8 y, x9 a...
 14.2.61: Work in a hyperbolic field Consider the hyperbolic force field F = ...
 14.2.62: 6263. Mass and density A thin wire represented by the smooth curve ...
 14.2.63: 6263. Mass and density A thin wire represented by the smooth curve ...
 14.2.64: Heat flux in a plate A square plate R = 51x, y2: 0 x 1, 0 y 16 has ...
 14.2.65: Inverse force fields Consider the radial field F = r _ r _p = 8x, y...
 14.2.66: Flux across curves in a vector field Consider the vector field F = ...
 14.2.67: Let R be the rectangle with vertices 10, 02, 1a, 02, 10, b2, and 1a...
 14.2.68: Let R = 51r, u2: 0 r a, 0 u 2p6 be the disk of radius a centered at...
Solutions for Chapter 14.2: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 14.2
Get Full SolutionsChapter 14.2 includes 68 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This expansive textbook survival guide covers the following chapters and their solutions. Since 68 problems in chapter 14.2 have been answered, more than 54225 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2.

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

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Continuous function
A function that is continuous on its entire domain

End behavior asymptote of a rational function
A polynomial that the function approaches as.

Feasible points
Points that satisfy the constraints in a linear programming problem.

Focal length of a parabola
The directed distance from the vertex to the focus.

Fundamental
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

Gaussian curve
See Normal curve.

Imaginary unit
The complex number.

Inverse cosecant function
The function y = csc1 x

Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Quadric surface
The graph in three dimensions of a seconddegree equation in three variables.

Real number line
A horizontal line that represents the set of real numbers.

Rectangular coordinate system
See Cartesian coordinate system.

Slope
Ratio change in y/change in x

Solution set of an inequality
The set of all solutions of an inequality

Terminal side of an angle
See Angle.

Vertical line test
A test for determining whether a graph is a function.