 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 Sieva Kozinsky and is associated to the ISBN: 9780321587992. Since 54 problems in chapter 15: Multiple Integrals have been answered, more than 3962 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.

Additive identity for the complex numbers
0 + 0i is the complex number zero

Angle of depression
The acute angle formed by the line of sight (downward) and the horizontal

Annual percentage rate (APR)
The annual interest rate

Arccosine function
See Inverse cosine function.

Binomial probability
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n  k2!pk11  p) nk where p is the probability of the outcome occurring once

Cotangent
The function y = cot x

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

Length of an arrow
See Magnitude of an arrow.

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

Logarithmic function with base b
The inverse of the exponential function y = bx, denoted by y = logb x

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

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Scalar
A real number.

Slope
Ratio change in y/change in x

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Standard form of a polynomial function
ƒ(x) = an x n + an1x n1 + Á + a1x + a0

Sum of an infinite series
See Convergence of a series

xyplane
The points x, y, 0 in Cartesian space.
I don't want to reset my password
Need help? Contact support
Having trouble accessing your account? Let us help you, contact support at +1(510) 9441054 or support@studysoup.com
Forgot password? Reset it here