 6.1: If C is the parabola y = 4 x 2 with 2 x 2, then C y sin x ds = 0.
 6.2: If F = i + j + k and C is the straight line from the origin to (2, ...
 6.3: If F = xi + yj + zk and C is the straight line from (3, 3, 3) to th...
 6.4: Suppose that f (x) > 0 for all x. Let F = f (x) i. If C is the hori...
 6.5: Suppose that f (x) > 0 for all x. Let F = f (x) i. If C is the vert...
 6.6: If x is a unitspeed path, then x F ds = b a (F v) ds, where v deno...
 6.7: If x and y are two oneone parametrizations of the same curve and F...
 6.8: If a nonvanishing, continuous vector field F is everywhere tangent ...
 6.9: If a nonvanishing, continuous vector field F is everywhere normal t...
 6.10: If the curve C is the level set at height c of a function f (x, y),...
 6.11: If f (x, y,z) is a continuous function and C f (x, y,z) ds = 0 for ...
 6.12: If a closed curve C is a level set of a function f (x, y) of class ...
 6.13: If a closed curve C is a level set of a function f (x, y) of class ...
 6.14: If a vector field F has constant magnitude 3 and makes a constant a...
 6.15: If F is a continuous vector field everywhere tangent to an oriented...
 6.16: If F is a constant vector field on R2, then C F ds = 0, where C is ...
 6.17: If F is an incompressible (i.e., divergenceless) C1 vector field on...
 6.18: If F is an incompressible C1 vector field on R2, then the flux acro...
 6.19: If C is a simple curve in R2, then C f ds = 0
 6.20: If C is a simple, closed curve in R2 and f is of class C1, then C f...
 6.21: F = (ex cos y + 3)i ex sin y j is a conservative vector field on R2.
 6.22: If f and g are functions of class C1 defined on a region D in R2, t...
 6.23: If C is a closed curve in R3 such that C F ds = 0, then F is conser...
 6.24: C x dx + y dy + z dz = 0 for all simple, closed curves C in R3
 6.25: C ex (cos y sin z dx + sin y sin z dy + cos y cosz) dz = 0 for all ...
 6.26: If F = 0, then F is conservative.
 6.27: Let M(x, y) and N(x, y) be C1 functions with domain R2 {(0, 0)}. If...
 6.28: Let M(x, y,z), N(x, y,z), and P(x, y,z) be C1 functions with domain...
 6.29: If F: Rn Rn, then there is at most one function f : R R such that f...
 6.30: If F is a differentiable vector field and F = G, then F = 0.
 6.31: A function g(x, y) is said to be harmonic at a point (x0, y0) if g ...
 6.32: A function g(x, y) is said to be harmonic at a point (x0, y0) if g ...
 6.33: A function g(x, y) is said to be harmonic at a point (x0, y0) if g ...
 6.34: We call a vector field F on R3 radially symmetric if it can be writ...
 6.35: Let F = y i + x j x 2 + y2 . (a) Verify Greens theorem over the ann...
 6.36: Considerthe vector fieldF = y x 2 + y2 i + x x 2 + y2 j. (a) Calcul...
 6.37: (a) Let F = ey i + x 4 j. Calculate the flux C F n ds of F across t...
 6.38: Use Newtons second law of motion F = ma to show that the work done ...
 6.39: Let F be a conservative vector field on R3 with F = V. If a particl...
Solutions for Chapter 6: Line Integrals
Full solutions for Vector Calculus  4th Edition
ISBN: 9780321780652
Solutions for Chapter 6: Line Integrals
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Vector Calculus was written by and is associated to the ISBN: 9780321780652. Chapter 6: Line Integrals includes 39 full stepbystep solutions. Since 39 problems in chapter 6: Line Integrals have been answered, more than 12652 students have viewed full stepbystep solutions from this chapter.

Compound fraction
A fractional expression in which the numerator or denominator may contain fractions

Conditional probability
The probability of an event A given that an event B has already occurred

Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian threedimensional space

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

DMS measure
The measure of an angle in degrees, minutes, and seconds

Equivalent arrows
Arrows that have the same magnitude and direction.

Fivenumber summary
The minimum, first quartile, median, third quartile, and maximum of a data set.

Future value of an annuity
The net amount of money returned from an annuity.

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Jump discontinuity at x a
limx:a  ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

kth term of a sequence
The kth expression in the sequence

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.

Randomization
The principle of experimental design that makes it possible to use the laws of probability when making inferences.

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Reflection through the origin
x, y and (x,y) are reflections of each other through the origin.

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Symmetric property of equality
If a = b, then b = a

Vertices of an ellipse
The points where the ellipse intersects its focal axis.