 15.15.1: In Exercises 14, sketch the region of integration and evaluate the...
 15.15.2: In Exercises 14, sketch the region of integration and evaluate the...
 15.15.3: In Exercises 14, sketch the region of integration and evaluate the...
 15.15.4: In Exercises 14, sketch the region of integration and evaluate the...
 15.15.5: In Exercises 58, sketch the region of integration and write an equ...
 15.15.6: In Exercises 58, sketch the region of integration and write an equ...
 15.15.7: In Exercises 58, sketch the region of integration and write an equ...
 15.15.8: In Exercises 58, sketch the region of integration and write an equ...
 15.15.9: Evaluate the integrals in Exercises 912. {' rz 4 cos (x2) dx dy 1
 15.15.10: Evaluate the integrals in Exercises 912. {2 (1 er' dx dy
 15.15.11: Evaluate the integrals in Exercises 912. o ~ y4 + 1
 15.15.12: Evaluate the integrals in Exercises 912. f sm 'If X dx dy
 15.15.13: Find the area of the region enclosed by the line y = 2x + 4 and the...
 15.15.14: Find the area of the ''triangular" region in the xyplane that is b...
 15.15.15: Find the volume under the psraholoid Z = x 2 + y2 above the triangl...
 15.15.16: Find the volume under the parabolic cylinder z = x2 above the regio...
 15.15.17: Find the average value of f(x, y) = xy over the regions in Exercise...
 15.15.18: Find the average value of f(x, y) = xy over the regions in Exercise...
 15.15.19: Evaluate the integrals in Exercises 19 and 20 by changing to polar ...
 15.15.20: Evaluate the integrals in Exercises 19 and 20 by changing to polar ...
 15.15.21: Integrate the function f(x, y) = I/O + x 2 + y2)2 over the region e...
 15.15.22: The triangle with vertices (0, 0), (1, 0), and (I, v3)
 15.15.23: Evaluate the integrals in Exercises 23 26.1"1"1" cos (x + Y + z) d...
 15.15.24: Evaluate the integrals in Exercises 23 26. in 710ln 21 In 5 24. e(...
 15.15.25: Evaluate the integrals in Exercises 23 26. 111x'1x+y(2x  y  z) d...
 15.15.26: Evaluate the integrals in Exercises 23 26. j elxlz2Y 26. 3dydzdx
 15.15.27: Find the volume of the wedgeshaped region enclosed on the side by ...
 15.15.28: Find the volume of the solid that is bounded above by the cylinder ...
 15.15.29: Find the average value of f(x,y,z) = 30xz ~ over the rectangular so...
 15.15.30: Find the average value of p over the solid sphere p ::s a ( spheric...
 15.15.31: Cylindrical to rectangular coordinates Convert (2" r./2!~ io io r 3...
 15.15.32: (a) Convert to cylindrical coordinates. Then (b) evaluate the new i...
 15.15.33: (a) Convert to spherical coordinates. Then (b) evaluate the new int...
 15.15.34: Write an iterated triple integral for the integral of f(x, y, z) = ...
 15.15.35: Set up an integral in rectangular coordinates equivalent to the int...
 15.15.36: The volume of a solid is 12iva x'iv 4 x' y' o 0 V4 x' y' dzdy...
 15.15.37: Triple integrals involving spherical shapes do not always require s...
 15.15.38: Find the moment of inertia about the zaxis of a solid of constant ...
 15.15.39: Find the moment of inertia of a solid of constant density 8 bounded...
 15.15.40: Find the moment of inertia about the zaxis of a solid of density 8...
 15.15.41: Find the centroid of the "triangular" region bounded by the lines x...
 15.15.42: Find the centroid of the region between the parabola x + y2  2y ~ ...
 15.15.43: Find the polar moment of inertia about the origin of a thin triangu...
 15.15.44: Find the polar moment of inertia about the center of a thin rectang...
 15.15.45: Find the moment of inertia about the xaxis of a thin plate of cons...
 15.15.46: Find the center of mass and the moments of inertia about the coordi...
 15.15.47: Find the mass and first moments about the coordinate axes of a thin...
 15.15.48: Find the moment of inertia about the xaxis of a thin triangular pl...
 15.15.49: Find the centroid of the region in the polar coordinate plane defin...
 15.15.50: Find the centroid of the region in the first quadrant bounded by th...
 15.15.51: Find the centroid of the region in the polar coordinate plane that ...
 15.15.52: Find the centroid of the plane region defined by the polar coordina...
 15.15.53: Show that if u ~ x  y and v ~ y, then
 15.15.54: What relationship must hold between the constants a, b, and c to ms...
Solutions for Chapter 15: Multiple Integrals
Full solutions for Thomas' Calculus  12th Edition
ISBN: 9780321587992
Solutions for Chapter 15: Multiple Integrals
Get Full SolutionsThomas' Calculus was written by and is associated to the ISBN: 9780321587992. Since 54 problems in chapter 15: Multiple Integrals have been answered, more than 8632 students have viewed full stepbystep solutions from this chapter. Chapter 15: Multiple Integrals includes 54 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Thomas' Calculus, edition: 12.

Arctangent function
See Inverse tangent function.

Common logarithm
A logarithm with base 10.

Complex plane
A coordinate plane used to represent the complex numbers. The xaxis of the complex plane is called the real axis and the yaxis is the imaginary axis

De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

Directed distance
See Polar coordinates.

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.

Inequality symbol or
<,>,<,>.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

Linear programming problem
A method of solving certain problems involving maximizing or minimizing a function of two variables (called an objective function) subject to restrictions (called constraints)

Magnitude of a real number
See Absolute value of a real number

Measure of an angle
The number of degrees or radians in an angle

Nappe
See Right circular cone.

Order of magnitude (of n)
log n.

Probability simulation
A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Summation notation
The series a nk=1ak, where n is a natural number ( or ?) is in summation notation and is read "the sum of ak from k = 1 to n(or infinity).” k is the index of summation, and ak is the kth term of the series

Symmetric matrix
A matrix A = [aij] with the property aij = aji for all i and j

Terminal side of an angle
See Angle.