 14.1: In Exercises 1 and 2, evaluate the integral.
 14.2: In Exercises 1 and 2, evaluate the integral.
 14.3: In Exercises 36, evaluate the iterated integral. Change the coordin...
 14.4: In Exercises 36, evaluate the iterated integral. Change the coordin...
 14.5: In Exercises 36, evaluate the iterated integral. Change the coordin...
 14.6: In Exercises 36, evaluate the iterated integral. Change the coordin...
 14.7: Area In Exercises 714, write the limits for the double integral for...
 14.8: Area In Exercises 714, write the limits for the double integral for...
 14.9: Area In Exercises 714, write the limits for the double integral for...
 14.10: Area In Exercises 714, write the limits for the double integral for...
 14.11: Area In Exercises 714, write the limits for the double integral for...
 14.12: Area In Exercises 714, write the limits for the double integral for...
 14.13: Area In Exercises 714, write the limits for the double integral for...
 14.14: Area In Exercises 714, write the limits for the double integral for...
 14.15: Think About It In Exercises 15 and 16, give a geometric argument fo...
 14.16: Think About It In Exercises 15 and 16, give a geometric argument fo...
 14.17: Volume In Exercises 17 and 18, use a multiple integral and a conven...
 14.18: Volume In Exercises 17 and 18, use a multiple integral and a conven...
 14.19: Approximation In Exercises 19 and 20, determine which value best ap...
 14.20: Approximation In Exercises 19 and 20, determine which value best ap...
 14.21: Probability In Exercises 21 and 22, find such that the function is ...
 14.22: Probability In Exercises 21 and 22, find such that the function is ...
 14.23: True or False? In Exercises 2326, determine whether the statement i...
 14.24: True or False? In Exercises 2326, determine whether the statement i...
 14.25: True or False? In Exercises 2326, determine whether the statement i...
 14.26: True or False? In Exercises 2326, determine whether the statement i...
 14.27: In Exercises 27 and 28, evaluate the iterated integral by convertin...
 14.28: In Exercises 27 and 28, evaluate the iterated integral by convertin...
 14.29: Volume In Exercises 29 and 30, use a multiple integral and a conven...
 14.30: Volume In Exercises 29 and 30, use a multiple integral and a conven...
 14.31: Consider the region in the plane bounded by the graph of the equati...
 14.32: Combine the sum of the two iterated integrals into a single iterate...
 14.33: Mass and Center of Mass In Exercises 33 and 34, find the mass and c...
 14.34: Mass and Center of Mass In Exercises 33 and 34, find the mass and c...
 14.35: In Exercises 35 and 36, find and for the lamina bounded by the grap...
 14.36: In Exercises 35 and 36, find and for the lamina bounded by the grap...
 14.37: Surface Area In Exercises 37 and 38, find the area of the surface g...
 14.38: Surface Area In Exercises 37 and 38, find the area of the surface g...
 14.39: Surface Area Find the area of the surface of the cylinder that lies...
 14.40: Surface Area The roof over the stage of an open air theater at a th...
 14.41: In Exercises 41 44, evaluate the iterated integral.
 14.42: In Exercises 41 44, evaluate the iterated integral.
 14.43: In Exercises 41 44, evaluate the iterated integral.
 14.44: In Exercises 41 44, evaluate the iterated integral.
 14.45: In Exercises 45 and 46, use a computer algebra system to evaluate t...
 14.46: In Exercises 45 and 46, use a computer algebra system to evaluate t...
 14.47: Volume In Exercises 47 and 48, use a multiple integral to find the ...
 14.48: Volume In Exercises 47 and 48, use a multiple integral to find the ...
 14.49: Center of Mass In Exercises 4952, find the center of mass of the so...
 14.50: Center of Mass In Exercises 4952, find the center of mass of the so...
 14.51: Center of Mass In Exercises 4952, find the center of mass of the so...
 14.52: Center of Mass In Exercises 4952, find the center of mass of the so...
 14.53: Moment of Inertia In Exercises 53 and 54, find the moment of inerti...
 14.54: Moment of Inertia In Exercises 53 and 54, find the moment of inerti...
 14.55: Investigation Consider a spherical segment of height from a sphere ...
 14.56: Moment of Inertia Find the moment of inertia about the axis of the ...
 14.57: In Exercises 57 and 58, give a geometric interpretation of the iter...
 14.58: In Exercises 57 and 58, give a geometric interpretation of the iter...
 14.59: In Exercises 59 and 60, find the Jacobian for the indicated change ...
 14.60: In Exercises 59 and 60, find the Jacobian for the indicated change ...
 14.61: In Exercises 61 and 62, use the indicated change of variables to ev...
 14.62: In Exercises 61 and 62, use the indicated change of variables to ev...
 14.1: (a) Find the volume of the solid of intersection of the three cylin...
 14.2: Let and be positive real numbers. The first octant of the plane is ...
 14.3: Derive Eulers famous result that was mentioned in Section 9.3, by c...
 14.4: Consider a circular lawn with a radius of 10 feet, as shown in the ...
 14.5: The figure shows the region bounded by the curves and Use the chang...
 14.6: The figure shows a solid bounded below by the plane and above by th...
 14.7: Sketch the solid whose volume is given by the sum of the iterated i...
 14.8: Prove that
 14.9: In Exercises 9 and 10, evaluate the integral. (Hint: See Exercise 5...
 14.10: In Exercises 9 and 10, evaluate the integral. (Hint: See Exercise 5...
 14.11: Consider the function Find the relationship between the positive co...
 14.12: From 1963 to 1986, the volume of the Great Salt Lake approximately ...
 14.13: The angle between a plane and the plane is where The projection of ...
 14.14: Use the result of Exercise 13 to order the planes in ascending orde...
 14.15: Evaluate the integral
 14.16: Evaluate the integrals and Are the results the same? Why or why not?
 14.17: Show that the volume of a spherical block can be approximated by
Solutions for Chapter 14: Multiple Integration
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 14: Multiple Integration
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus, edition: 8. Calculus was written by and is associated to the ISBN: 9780618502981. Chapter 14: Multiple Integration includes 79 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 79 problems in chapter 14: Multiple Integration have been answered, more than 76554 students have viewed full stepbystep solutions from this chapter.

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

Components of a vector
See Component form of a vector.

Doubleangle identity
An identity involving a trigonometric function of 2u

Equilibrium point
A point where the supply curve and demand curve intersect. The corresponding price is the equilibrium price.

First quartile
See Quartile.

Fitting a line or curve to data
Finding a line or curve that comes close to passing through all the points in a scatter plot.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Initial side of an angle
See Angle.

kth term of a sequence
The kth expression in the sequence

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Multiplicative identity for matrices
See Identity matrix

Objective function
See Linear programming problem.

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

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Right angle
A 90° angle.

Speed
The magnitude of the velocity vector, given by distance/time.

Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.

Zero vector
The vector <0,0> or <0,0,0>.