 15.7.1: Evaluate the integral in Example 1, integrating first with respect ...
 15.7.2: Evaluate the integral , where using three different orders of integ...
 15.7.3: Evaluate the iterated integral.
 15.7.4: Evaluate the iterated integral.
 15.7.5: Evaluate the iterated integral.
 15.7.6: Evaluate the iterated integral.
 15.7.7: Evaluate the iterated integral.
 15.7.8: Evaluate the iterated integral.
 15.7.9: Evaluate the triple integral.
 15.7.10: Evaluate the triple integral.
 15.7.11: Evaluate the triple integral.
 15.7.12: Evaluate the triple integral.
 15.7.13: Evaluate the triple integral.
 15.7.14: Evaluate the triple integral.
 15.7.15: Evaluate the triple integral.
 15.7.16: Evaluate the triple integral.
 15.7.17: Evaluate the triple integral.
 15.7.18: Evaluate the triple integral.
 15.7.19: Use a triple integral to find the volume of the given solid. The te...
 15.7.20: Use a triple integral to find the volume of the given solid. The so...
 15.7.21: Use a triple integral to find the volume of the given solid. The so...
 15.7.22: Use a triple integral to find the volume of the given solid. The so...
 15.7.23: (a) Express the volume of the wedge in the first octant that is cut...
 15.7.24: (a) In the Midpoint Rule for triple integrals we use a triple Riema...
 15.7.25: Use the Midpoint Rule for triple integrals (Exer cise 24) to estima...
 15.7.26: Use the Midpoint Rule for triple integrals (Exer cise 24) to estima...
 15.7.27: Sketch the solid whose volume is given by the iterated integral.
 15.7.28: Sketch the solid whose volume is given by the iterated integral.
 15.7.29: Express the integral as an iterated integral in six different ways,...
 15.7.30: Express the integral as an iterated integral in six different ways,...
 15.7.31: Express the integral as an iterated integral in six different ways,...
 15.7.32: Express the integral as an iterated integral in six different ways,...
 15.7.33: The figure shows the region of integration for the integral Rewrite...
 15.7.34: The figure shows the region of integration for the integral Rewrite...
 15.7.35: Write five other iterated integrals that are equal to the given ite...
 15.7.36: Write five other iterated integrals that are equal to the given ite...
 15.7.37: Evaluate the triple integral using only geometric interpretation an...
 15.7.38: Evaluate the triple integral using only geometric interpretation an...
 15.7.39: Find the mass and center of mass of the solid with the given densit...
 15.7.40: Find the mass and center of mass of the solid with the given densit...
 15.7.41: Find the mass and center of mass of the solid with the given densit...
 15.7.42: Find the mass and center of mass of the solid with the given densit...
 15.7.43: Assume that the solid has constant density . Find the moments of in...
 15.7.44: Assume that the solid has constant density . Find the moments of in...
 15.7.45: Assume that the solid has constant density . Find the moment of ine...
 15.7.46: Assume that the solid has constant density . Find the moment of ine...
 15.7.47: Set up, but do not evaluate, integral expressions for (a) the mass,...
 15.7.48: Set up, but do not evaluate, integral expressions for (a) the mass,...
 15.7.49: Let be the solid in the first octant bounded by the cylinder and th...
 15.7.50: If is the solid of Exercise 18 with density function , find the fol...
 15.7.51: The joint density function for random variables , , and is if , and...
 15.7.52: Suppose , , and are random variables with joint density function if...
 15.7.53: The average value of a function over a solid region is defined to b...
 15.7.54: The average value of a function over a solid region is defined to b...
 15.7.55: The average value of a function over a solid region is defined to b...
Solutions for Chapter 15.7: TRIPLE INTEGRALS
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 15.7: TRIPLE INTEGRALS
Get Full SolutionsChapter 15.7: TRIPLE INTEGRALS includes 55 full stepbystep solutions. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879. Since 55 problems in chapter 15.7: TRIPLE INTEGRALS have been answered, more than 21854 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

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

Continuous function
A function that is continuous on its entire domain

Cotangent
The function y = cot x

Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Inferential statistics
Using the science of statistics to make inferences about the parameters in a population from a sample.

Infinite sequence
A function whose domain is the set of all natural numbers.

Integrable over [a, b] Lba
ƒ1x2 dx exists.

kth term of a sequence
The kth expression in the sequence

Main diagonal
The diagonal from the top left to the bottom right of a square matrix

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

Natural logarithm
A logarithm with base e.

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Repeated zeros
Zeros of multiplicity ? 2 (see Multiplicity).

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Terms of a sequence
The range elements of a sequence.

Transverse axis
The line segment whose endpoints are the vertices of a hyperbola.

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

Zero matrix
A matrix consisting entirely of zeros.