 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 3075 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 inverse of a real number
The opposite of b , or b

Arccotangent function
See Inverse cotangent function.

Categorical variable
In statistics, a nonnumerical variable such as gender or hair color. Numerical variables like zip codes, in which the numbers have no quantitative significance, are also considered to be categorical.

Distance (in a coordinate plane)
The distance d(P, Q) between P(x, y) and Q(x, y) d(P, Q) = 2(x 1  x 2)2 + (y1  y2)2

Divisor of a polynomial
See Division algorithm for polynomials.

Doubleangle identity
An identity involving a trigonometric function of 2u

First quartile
See Quartile.

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Natural exponential function
The function ƒ1x2 = ex.

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

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

Radian measure
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Removable discontinuity at x = a
lim x:a ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

Right triangle
A triangle with a 90° angle.

Sample space
Set of all possible outcomes of an experiment.

System
A set of equations or inequalities.

Vertical stretch or shrink
See Stretch, Shrink.
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