 16.16.1: The accompanying figore shows two polygonal paths in space joining ...
 16.16.2: The accompanying figure shows three polygonal paths joining the ori...
 16.16.3: Integrate f(x,y, z) = ~ over the circle r(t) = (a cos t)j + (a sin ...
 16.16.4: Integrate f(x, y, z) = v' x 2 + y2 over the involute curve r(t) = (...
 16.16.5: Evaluate the integrals in Exercises 5 and 6.
 16.16.6: Evaluate the integrals in Exercises 5 and 6.
 16.16.7: Integrate F = (ysinz)i + (xsinz)j + (xycosz)k around the circle cu...
 16.16.8: Integrate F = 3x2yi + (x 3 + l)j + 9z2k around the circle cut from ...
 16.16.9: Evaluate the integrals in Exercises 9 and 10. 1sxsinydx  SycosxdyC...
 16.16.10: Evaluate the integrals in Exercises 9 and 10. 1y2 dx + x 2 dyC is t...
 16.16.11: Find the area of the elliptical region cut from the plane x + y + z...
 16.16.12: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by th...
 16.16.13: Find the area of the cap cut from the top of the sphere x 2 + y2 + ...
 16.16.14: a. Hemisphere cut by cylinder Find the area of the surface cut from...
 16.16.15: Find the area of the triangle in which the plane (x/a) + (y/b) + (z...
 16.16.16: Integrate yz a. g(x,y,z) = ~r /~= v4y2 + 1 b. g(x,y,z) = v'4Y~ + 1...
 16.16.17: Integrate g(x, y, z) = x 4y(y2 + z2) over the portion of the cylind...
 16.16.18: The state of Wyoming is bounded by the meridians 111 3 / and 1043/ ...
 16.16.19: Find parametrizations for the surfaces in Exercises 19 24. (There ...
 16.16.20: Find parametrizations for the surfaces in Exercises 19 24. (There ...
 16.16.21: Find parametrizations for the surfaces in Exercises 19 24. (There ...
 16.16.22: Find parametrizations for the surfaces in Exercises 19 24. (There ...
 16.16.23: Find parametrizations for the surfaces in Exercises 19 24. (There ...
 16.16.24: Find parametrizations for the surfaces in Exercises 19 24. (There ...
 16.16.25: The portion of the paraboloid y = 2(x2 + z2), y :5 2, that lies abo...
 16.16.26: Integrate /(x,y,z) = xy  z2 over the sur face in Exercise 25
 16.16.27: Find the surface area of the helicoid r(r, 6) = (r cos 6)i + (rsin ...
 16.16.28: Evaluate the integral ffs v'x2 + y2 + I du, wbere S is the helicoid...
 16.16.29: Which of the fields in Exercises 2932 are conservative, and which ...
 16.16.30: Which of the fields in Exercises 2932 are conservative, and which ...
 16.16.31: Which of the fields in Exercises 2932 are conservative, and which ...
 16.16.32: Which of the fields in Exercises 2932 are conservative, and which ...
 16.16.33: Find potential functions for the fields in Exercises 33 and 34. F =...
 16.16.34: Find potential functions for the fields in Exercises 33 and 34. F =...
 16.16.35: In Exercises 35 and 36, Imd the work done by each field along the p...
 16.16.36: In Exercises 35 and 36, Imd the work done by each field along the p...
 16.16.37: Find the work done by xi + yj F = C;;C,,= (x2 + y2)'/2 over th...
 16.16.38: Find the flow of the field F = V(x2 ze') a. once around the ellipse...
 16.16.39: In Exercises 39 and 40, use the surface integral in Stokes' Theorem...
 16.16.40: In Exercises 39 and 40, use the surface integral in Stokes' Theorem...
 16.16.41: Find the mass of a thin wire lying along the curve r(l) = v2ti + v2...
 16.16.42: Find the center of mass of a thin wire lying along the curve r(l) =...
 16.16.43: Find the ceoter of mass and the momeots of inertia aboot the coordi...
 16.16.44: A slender metal arch lies along the semicircle y = v' a2  x 2 in t...
 16.16.45: A wire of constant density B = 1 lies along the curve r(l) = (e' co...
 16.16.46: Find the mass and center of mass of a wire of constant density B th...
 16.16.47: Find I. and the center of mass of a thin shell of density B(x, y, z...
 16.16.48: Find the moment of inertia about the zaxis of the surface of the c...
 16.16.49: Use Green's Theorem to Imd the counterclockwise circulation and oot...
 16.16.50: Use Green's Theorem to Imd the counterclockwise circulation and oot...
 16.16.51: Show that f cosy lnxsinyt(y  xtix ~ 0 c for any closed curve C t...
 16.16.52: Show that tire outward flux of the position vector field F = xi + y...
 16.16.53: In Exercises 5356, fmd tire outward flux of F across tire bouodary...
 16.16.54: In Exercises 5356, fmd tire outward flux of F across tire bouodary...
 16.16.55: In Exercises 5356, fmd tire outward flux of F across tire bouodary...
 16.16.56: In Exercises 5356, fmd tire outward flux of F across tire bouodary...
 16.16.57: Let S he the surface that is bounded on tire leftby the hemisphere ...
 16.16.58: Find the outward flux of the fteld F ~ 3X2'i + yj  z'k across the ...
 16.16.59: Use the Divergence Theorem to fmd the flux ofF ~ xy'i + x'yj + yk o...
 16.16.60: Find the flux ofF ~ (3z + I)kupwardacrossthe hemisphere x 2 + y2 + ...
Solutions for Chapter 16: Integration in Vector Fields
Full solutions for Thomas' Calculus  12th Edition
ISBN: 9780321587992
Solutions for Chapter 16: Integration in Vector Fields
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 60 problems in chapter 16: Integration in Vector Fields have been answered, more than 4036 students have viewed full stepbystep solutions from this chapter. Thomas' Calculus was written by Sieva Kozinsky and is associated to the ISBN: 9780321587992. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12. Chapter 16: Integration in Vector Fields includes 60 full stepbystep solutions.

Arithmetic sequence
A sequence {an} in which an = an1 + d for every integer n ? 2 . The number d is the common difference.

Census
An observational study that gathers data from an entire population

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Elements of a matrix
See Matrix element.

Ellipse
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant

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.

Exponential form
An equation written with exponents instead of logarithms.

Interval notation
Notation used to specify intervals, pp. 4, 5.

Inverse variation
See Power function.

Law of cosines
a2 = b2 + c2  2bc cos A, b2 = a2 + c2  2ac cos B, c2 = a2 + b2  2ab cos C

Line graph
A graph of data in which consecutive data points are connected by line segments

Linear regression
A procedure for finding the straight line that is the best fit for the data

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

Orthogonal vectors
Two vectors u and v with u x v = 0.

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Real zeros
Zeros of a function that are real numbers.

Resistant measure
A statistical measure that does not change much in response to outliers.

Variance
The square of the standard deviation.

Vector
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.
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