 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, sketch the region of integration. Thenevaluate the...
 14.4: In Exercises 36, sketch the region of integration. Thenevaluate the...
 14.5: In Exercises 36, sketch the region of integration. Thenevaluate the...
 14.6: In Exercises 36, sketch the region of integration. Thenevaluate the...
 14.7: In Exercises 714, write the limits for the double integral Rf x, y ...
 14.8: In Exercises 714, write the limits for the double integral Rf x, y ...
 14.9: In Exercises 714, write the limits for the double integral Rf x, y ...
 14.10: In Exercises 714, write the limits for the double integral Rf x, y ...
 14.11: In Exercises 714, write the limits for the double integral Rf x, y ...
 14.12: In Exercises 714, write the limits for the double integral Rf x, y ...
 14.13: In Exercises 714, write the limits for the double integral Rf x, y ...
 14.14: In Exercises 714, write the limits for the double integral Rf x, y ...
 14.15: Think About It In Exercises 15 and 16, give a geometric argumentfor...
 14.16: Think About It In Exercises 15 and 16, give a geometric argumentfor...
 14.17: Volume In Exercises 17 and 18, use a multiple integral and aconveni...
 14.18: Volume In Exercises 17 and 18, use a multiple integral and aconveni...
 14.19: Average Value In Exercises 19 and 20, find the average ofover the r...
 14.20: Average Value In Exercises 19 and 20, find the average ofover the r...
 14.21: Average Temperature The temperature in degrees Celsius onthe surfac...
 14.22: Average Profit A firms profit from marketing two softdrinks iswhere...
 14.23: Probability In Exercises 23 and 24, find such that thefunction is a...
 14.24: Probability In Exercises 23 and 24, find such that thefunction is a...
 14.25: Approximation In Exercises 25 and 26, determine which valuebest app...
 14.26: Approximation In Exercises 25 and 26, determine which valuebest app...
 14.27: True or False? In Exercises 2730, determine whether thestatement is...
 14.28: True or False? In Exercises 2730, determine whether thestatement is...
 14.29: True or False? In Exercises 2730, determine whether thestatement is...
 14.30: True or False? In Exercises 2730, determine whether thestatement is...
 14.31: Exercises 31 and 32, evaluate the iterated integral byconverting to...
 14.32: Exercises 31 and 32, evaluate the iterated integral byconverting to...
 14.33: Area In Exercises 33 and 34, use a double integral to find thearea ...
 14.34: Area In Exercises 33 and 34, use a double integral to find thearea ...
 14.35: Volume In Exercises 35 and 36, use a multiple integral and aconveni...
 14.36: Volume In Exercises 35 and 36, use a multiple integral and aconveni...
 14.37: Consider the region in the plane bounded by the graph ofthe equatio...
 14.38: Combine the sum of the two iterated integrals into a singleiterated...
 14.39: Mass and Center of Mass In Exercises 39 and 40, find the massand ce...
 14.40: Mass and Center of Mass In Exercises 39 and 40, find the massand ce...
 14.41: In Exercises 41 and 42, find and for the laminabounded by the graph...
 14.42: In Exercises 41 and 42, find and for the laminabounded by the graph...
 14.43: Surface Area In Exercises 4346, find the area of the surfacegiven b...
 14.44: Surface Area In Exercises 4346, find the area of the surfacegiven b...
 14.45: Surface Area In Exercises 4346, find the area of the surfacegiven b...
 14.46: Surface Area In Exercises 4346, find the area of the surfacegiven b...
 14.47: Building Design A new auditorium is built with a foundationin the s...
 14.48: Surface Area The roof over the stage of an open air theater ata the...
 14.49: In Exercises 4952, evaluate the iterated integral.
 14.50: In Exercises 4952, evaluate the iterated integral.
 14.51: In Exercises 4952, evaluate the iterated integral.
 14.52: In Exercises 4952, evaluate the iterated integral.
 14.53: In Exercises 53 and 54, use a computer algebra system toevaluate th...
 14.54: In Exercises 53 and 54, use a computer algebra system toevaluate th...
 14.55: Volume In Exercises 55 and 56, use a multiple integral to findthe v...
 14.56: Volume In Exercises 55 and 56, use a multiple integral to findthe v...
 14.57: Center of Mass In Exercises 5760, find the center of massof the sol...
 14.58: Center of Mass In Exercises 5760, find the center of massof the sol...
 14.59: Center of Mass In Exercises 5760, find the center of massof the sol...
 14.60: Center of Mass In Exercises 5760, find the center of massof the sol...
 14.61: Moment of Inertia In Exercises 61 and 62, find the moment ofinertia...
 14.62: Moment of Inertia In Exercises 61 and 62, find the moment ofinertia...
 14.63: Investigation Consider a spherical segment of height froma sphere o...
 14.64: Moment of Inertia Find the moment of inertia about theaxis of the e...
 14.65: In Exercises 65 and 66, give a geometric interpretation of theitera...
 14.66: In Exercises 65 and 66, give a geometric interpretation of theitera...
 14.67: In Exercises 67 and 68, find the Jacobian for theindicated change o...
 14.68: In Exercises 67 and 68, find the Jacobian for theindicated change o...
 14.69: In Exercises 69 and 70, use the indicated change of variables toeva...
 14.70: In Exercises 69 and 70, use the indicated change of variables toeva...
Solutions for Chapter 14: Multiple Integration
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 14: Multiple Integration
Get Full SolutionsCalculus was written by and is associated to the ISBN: 9780547167022. Since 70 problems in chapter 14: Multiple Integration have been answered, more than 63975 students have viewed full stepbystep solutions from this chapter. Chapter 14: Multiple Integration includes 70 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus , edition: 9.

Arccosecant function
See Inverse cosecant function.

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Constant
A letter or symbol that stands for a specific number,

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

Discriminant
For the equation ax 2 + bx + c, the expression b2  4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2  4AC

Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

Graphical model
A visible representation of a numerical or algebraic model.

Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible

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

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Parametric curve
The graph of parametric equations.

Partial sums
See Sequence of partial sums.

Positive angle
Angle generated by a counterclockwise rotation.

Quadratic equation in x
An equation that can be written in the form ax 2 + bx + c = 01a ? 02

Quantitative variable
A variable (in statistics) that takes on numerical values for a characteristic being measured.

Radicand
See Radical.

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

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

Xmax
The xvalue of the right side of the viewing window,.