 16.2.1: What is the line integral of the constant function f (x, y, z) = 10...
 16.2.2: Which of the following have a zero line integral over the vertical ...
 16.2.3: State whether each statement is true or false. If the statement is ...
 16.2.4: Suppose that C has length 5. What is the value of C F dr if:
 16.2.5: In Exercises 58, compute the integral of the scalar function or vec...
 16.2.6: In Exercises 58, compute the integral of the scalar function or vec...
 16.2.7: In Exercises 58, compute the integral of the scalar function or vec...
 16.2.8: In Exercises 58, compute the integral of the scalar function or vec...
 16.2.9: In Exercises 916, compute C f ds for the curve specified. f (x, y) ...
 16.2.10: In Exercises 916, compute C f ds for the curve specified. (x, y) = ...
 16.2.11: In Exercises 916, compute C f ds for the curve specified. f (x, y, ...
 16.2.12: In Exercises 916, compute C f ds for the curve specified. f (x, y, ...
 16.2.13: In Exercises 916, compute C f ds for the curve specified. f (x, y, ...
 16.2.14: In Exercises 916, compute C f ds for the curve specified. f (x, y, ...
 16.2.15: In Exercises 916, compute C f ds for the curve specified. f (x, y, ...
 16.2.16: In Exercises 916, compute C f ds for the curve specified. f (x, y, ...
 16.2.17: Calculate C 1 ds, where the curve C is parametrized by r(t) = (4t, ...
 16.2.18: Calculate C 1 ds, where the curve C is parametrized by r(t) = (et, ...
 16.2.19: In Exercises 1926, compute C F dr for the oriented curve specified....
 16.2.20: In Exercises 1926, compute C F dr for the oriented curve specified....
 16.2.21: In Exercises 1926, compute C F dr for the oriented curve specified....
 16.2.22: In Exercises 1926, compute C F dr for the oriented curve specified....
 16.2.23: In Exercises 1926, compute C F dr for the oriented curve specified....
 16.2.24: In Exercises 1926, compute C F dr for the oriented curve specified....
 16.2.25: In Exercises 1926, compute C F dr for the oriented curve specified....
 16.2.26: In Exercises 1926, compute C F dr for the oriented curve specified....
 16.2.27: In Exercises 2732, evaluate the line integral. 27. C ydx xdy, parab...
 16.2.28: In Exercises 2732, evaluate the line integral.C ydx + zdy + xdz, r(...
 16.2.29: In Exercises 2732, evaluate the line integral.C (x y)dx + (y z)dy +...
 16.2.30: In Exercises 2732, evaluate the line integral.C zdx + x2 dy + ydz, ...
 16.2.31: In Exercises 2732, evaluate the line integral.C ydx + xdy x2 + y2 ,...
 16.2.32: In Exercises 2732, evaluate the line integral.C y2dx + z2dy + (1 x2...
 16.2.33: Let f (x, y, z) = x1yz, and let C be the curve parametrized by r(t)...
 16.2.34: Use a CAS to calculate C exy , ex+y dr to four decimal places, wher...
 16.2.35: The blue path from P to Q in Figure 14
 16.2.36: The closed path ABCA in Figure 15 z y x C = (0, 0, 6) A = (2, 0, 0)...
 16.2.37: In Exercises 37 and 38, C is the path from P to Q in Figure 16 that...
 16.2.38: In Exercises 37 and 38, C is the path from P to Q in Figure 16 that...
 16.2.39: The values of a function f (x, y, z) and vector field F(x, y, z) ar...
 16.2.40: Estimate the line integrals of f (x, y) and F(x, y) along the quart...
 16.2.41: Determine whether the line integrals of the vector fields around th...
 16.2.42: Determine whether the line integrals of the vector fields along the...
 16.2.43: Calculate the total mass of a circular piece of wire of radius 4 cm...
 16.2.44: Calculate the total mass of a metal tube in the helical shape r(t) ...
 16.2.45: Find the total charge on the curve y = x4/3 for 1 x 8 (in centimete...
 16.2.46: Find the total charge on the curve r(t) = (sin t, cost,sin2 t) in c...
 16.2.47: In Exercises 4750, use Eq. (6) to compute the electric potential V ...
 16.2.48: In Exercises 4750, use Eq. (6) to compute the electric potential V ...
 16.2.49: In Exercises 4750, use Eq. (6) to compute the electric potential V ...
 16.2.50: In Exercises 4750, use Eq. (6) to compute the electric potential V ...
 16.2.51: Calculate the work done by a field F = x + y,x y when an object mov...
 16.2.52: In Exercises 5254, calculate the work done by the field F when the...
 16.2.53: In Exercises 5254, calculate the work done by the field F when the...
 16.2.54: In Exercises 5254, calculate the work done by the field F when the...
 16.2.55: Figure 21 shows a force field F. (a) Over which of the two paths, A...
 16.2.56: Verify that the work performed along the segment PQ by the constant...
 16.2.57: Show that work performed by a constant force field F over any path ...
 16.2.58: Note that a curve C in polar form r = f () is parametrized by r() =...
 16.2.59: Charge is distributed along the spiral with polar equation r = for ...
 16.2.60: In Exercises 6063, let F be the vortex field (socalled because it ...
 16.2.61: In Exercises 6063, let F be the vortex field (socalled because it ...
 16.2.62: In Exercises 6063, let F be the vortex field (socalled because it ...
 16.2.63: In Exercises 6063, let F be the vortex field (socalled because it ...
 16.2.64: In Exercises 6467, use Eq. (10) to calculate the flux of the vector...
 16.2.65: In Exercises 6467, use Eq. (10) to calculate the flux of the vector...
 16.2.66: In Exercises 6467, use Eq. (10) to calculate the flux of the vector...
 16.2.67: In Exercises 6467, use Eq. (10) to calculate the flux of the vector...
 16.2.68: Let I = C f (x, y, z) ds. Assume that f (x, y, z) m for some number...
 16.2.69: Let F(x, y) = x, 0. Prove that if C is any path from (a, b) to (c, ...
 16.2.70: Let F(x, y) = y,x. Prove that if C is any path from (a, b) to (c, d...
 16.2.71: We wish to define the average value Av(f ) of a continuous function...
 16.2.72: Use Eq. (11) to calculate the average value of f (x, y) = x y along...
 16.2.73: Use Eq. (11) to calculate the average value of f (x, y) = x along t...
 16.2.74: The temperature (in degrees centigrade) at a point P on a circular ...
 16.2.75: The value of a scalar line integral does not depend on the choice o...
Solutions for Chapter 16.2: Line Integrals
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 16.2: Line Integrals
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 75 problems in chapter 16.2: Line Integrals have been answered, more than 40892 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. Chapter 16.2: Line Integrals includes 75 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885.

Arccosine function
See Inverse cosine function.

Argument of a complex number
The argument of a + bi is the direction angle of the vector {a,b}.

artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in threedimensional space and ordered triples of real numbers

Branches
The two separate curves that make up a hyperbola

Center
The central point in a circle, ellipse, hyperbola, or sphere

Commutative properties
a + b = b + a ab = ba

Cubic
A degree 3 polynomial function

Hypotenuse
Side opposite the right angle in a right triangle.

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Inequality symbol or
<,>,<,>.

Inverse cosine function
The function y = cos1 x

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

Partial fractions
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

Partial sums
See Sequence of partial sums.

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Product of functions
(ƒg)(x) = ƒ(x)g(x)

Response variable
A variable that is affected by an explanatory variable.

Sequence
See Finite sequence, Infinite sequence.

Terminal point
See Arrow.

Unbounded interval
An interval that extends to ? or ? (or both).