 14.1.1: The double integral is defined as a limit of Riemann sumsby Rf(x, y...
 14.1.2: The iterated integral 51 42f(x, y) dx dyintegrates f over the recta...
 14.1.3: Supply the missing integrand and limits of integration. 51 42(3x2 2...
 14.1.4: The volume of the solid enclosed by the surface z = x/yand the rect...
 14.1.5: 112 Evaluate the iterated integrals. ln 30 ln 20ex+y dy dx 6.
 14.1.6: 112 Evaluate the iterated integrals. 20 10y sin x dy dx7
 14.1.7: 112 Evaluate the iterated integrals. 01 52dx dy 8.
 14.1.8: 112 Evaluate the iterated integrals. 64 73dy dx9
 14.1.9: 112 Evaluate the iterated integrals. 10 10x(xy + 1)2 dy dx 10
 14.1.10: 112 Evaluate the iterated integrals. /2 21x cos xy dy dx1
 14.1.11: 112 Evaluate the iterated integrals. ln 20 10xyey2x dy dx 12
 14.1.12: 112 Evaluate the iterated integrals. 43 211(x + y)2 dy dx1
 14.1.13: 1316 Evaluate the double integral over the rectangular region R. R4...
 14.1.14: 1316 Evaluate the double integral over the rectangular region R. Rx...
 14.1.15: 1316 Evaluate the double integral over the rectangular region R. Rx...
 14.1.16: 1316 Evaluate the double integral over the rectangular region R. R(...
 14.1.17: (a) Let f(x, y) = x2 + y, and as shown in the accompanyingfigure, l...
 14.1.18: (a) Let f(x, y) = x 2y, and as shown in Exercise 17,let the rectang...
 14.1.19: 1920 Each iterated integral represents the volume of asolid. Make a...
 14.1.20: 1920 Each iterated integral represents the volume of asolid. Make a...
 14.1.21: 2122 Each iterated integral represents the volume of asolid. Make a...
 14.1.22: 2122 Each iterated integral represents the volume of asolid. Make a...
 14.1.23: 2326 TrueFalse Determine whether the statement is true orfalse. Exp...
 14.1.24: 2326 TrueFalse Determine whether the statement is true orfalse. Exp...
 14.1.25: 2326 TrueFalse Determine whether the statement is true orfalse. Exp...
 14.1.26: 2326 TrueFalse Determine whether the statement is true orfalse. Exp...
 14.1.27: In this exercise, suppose that f(x, y) = g(x)h(y) andR = {(x, y) : ...
 14.1.28: Use the result in Exercise 27 to evaluate the integral ln 20 11ey +...
 14.1.29: 2932 Use a double integral to find the volume. The volume under the...
 14.1.30: 2932 Use a double integral to find the volume. The volume under the...
 14.1.31: 2932 Use a double integral to find the volume. The volume of the so...
 14.1.32: 2932 Use a double integral to find the volume. The volume in the fi...
 14.1.33: Evaluate the integral by choosing a convenient order ofintegration:...
 14.1.34: (a) Sketch the solid in the first octant that is enclosedby the pla...
 14.1.35: 3540 The average value or mean value of a continuous functionf(x, y...
 14.1.36: 3540 The average value or mean value of a continuous functionf(x, y...
 14.1.37: 3540 The average value or mean value of a continuous functionf(x, y...
 14.1.38: 3540 The average value or mean value of a continuous functionf(x, y...
 14.1.39: 3540 The average value or mean value of a continuous functionf(x, y...
 14.1.40: 3540 The average value or mean value of a continuous functionf(x, y...
 14.1.41: 4142 Most computer algebra systems have commands for approximatingd...
 14.1.42: 4142 Most computer algebra systems have commands for approximatingd...
 14.1.43: Use a CAS to evaluate the iterated integrals 10 10y x(x + y)3 dx dy...
 14.1.44: Use a CAS to show that the volume V under the surfacez = xy3 sin xy...
 14.1.45: Writing Discuss how computing a volume using an iterateddouble inte...
 14.1.46: Writing Discuss how the double integral property givenin Formula (1...
Solutions for Chapter 14.1: DOUBLE INTEGRALS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 14.1: DOUBLE INTEGRALS
Get Full SolutionsCalculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Chapter 14.1: DOUBLE INTEGRALS includes 46 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: Early Transcendentals, , edition: 10. Since 46 problems in chapter 14.1: DOUBLE INTEGRALS have been answered, more than 39815 students have viewed full stepbystep solutions from this chapter.

Annual percentage yield (APY)
The rate that would give the same return if interest were computed just once a year

Annuity
A sequence of equal periodic payments.

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

equation of a hyperbola
(x  h)2 a2  (y  k)2 b2 = 1 or (y  k)2 a2  (x  h)2 b2 = 1

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

Event
A subset of a sample space.

Identity properties
a + 0 = a, a ? 1 = a

Implied domain
The domain of a function’s algebraic expression.

Linear system
A system of linear equations

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

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

Orthogonal vectors
Two vectors u and v with u x v = 0.

Polar axis
See Polar coordinate system.

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Reference angle
See Reference triangle

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

Root of a number
See Principal nth root.

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>

Tangent line of ƒ at x = a
The line through (a, ƒ(a)) with slope ƒ'(a) provided ƒ'(a) exists.

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