 5.1: Evaluate the integrals in Exercises 1 to 4.30x2+1x2+1xy dy dx
 5.2: Evaluate the integrals in Exercises 1 to 4.101x(x + y)2dy dx
 5.3: Evaluate the integrals in Exercises 1 to 4.10e2xexx ln y dydx
 5.4: Evaluate the integrals in Exercises 1 to 4.102132cos [(x + y + z)] ...
 5.5: Reverse the order of integration of the integrals in Exercises 5 to...
 5.6: Reverse the order of integration of the integrals in Exercises 5 to...
 5.7: Reverse the order of integration of the integrals in Exercises 5 to...
 5.8: Reverse the order of integration of the integrals in Exercises 5 to...
 5.9: Evaluate the integral J0(y + xz) dz dydx.
 5.10: Evaluate ex/y dxdy.
 5.11: Evaluate f0 fj^2" y/yycos xydxdy.
 5.12: Change the order of integration and evaluate (x + y)2 dxdy.0 y/2
 5.13: Show that evaluatingD dx dy, where D is a ysimpleregion, reproduce...
 5.14: Change the order of integration and evaluate(x2 + y3x) dxdy.0 y2/2
 5.15: Let D be the region in the xy plane inside the unit circle x2 + y2 ...
 5.16: fm/IdM2 cos (nx/4) ] dxdy, where D is the region in Figure 5.R.1.
 5.17: Evaluate the integrals in Exercises 17 to 24. Sketch and identify t...
 5.18: Evaluate the integrals in Exercises 17 to 24. Sketch and identify t...
 5.19: Evaluate the integrals in Exercises 17 to 24. Sketch and identify t...
 5.20: Evaluate the integrals in Exercises 17 to 24. Sketch and identify t...
 5.21: Evaluate the integrals in Exercises 17 to 24. Sketch and identify t...
 5.22: Evaluate the integrals in Exercises 17 to 24. Sketch and identify t...
 5.23: Evaluate the integrals in Exercises 17 to 24. Sketch and identify t...
 5.24: Evaluate the integrals in Exercises 17 to 24. Sketch and identify t...
 5.25: In Exercises 25 to 27, integrate the given function f over the give...
 5.26: In Exercises 25 to 27, integrate the given function f over the give...
 5.27: In Exercises 25 to 27, integrate the given function f over the give...
 5.28: In Exercises 28 and 29, sketch the region of integration, interchan...
 5.29: In Exercises 28 and 29, sketch the region of integration, interchan...
 5.30: Show that4e5 [1,3][2,4]ex2+y2dA 4e25.
 5.31: Show that4 D(x2 + y2 + 1) dx dy 20,where D is the disk of radius 2 ...
 5.32: Suppose W is a pathconnected region; that is, givenany two points ...
 5.33: Prove:x0 [t0 F(u) du] dt =x0 (x u)F(u) du.
 5.34: Evaluate the integrals in Exercises 34 to 36.10z0y0xy2z3dx dy dz
 5.35: Evaluate the integrals in Exercises 34 to 36.10y0x/30xx2 + z2 dz dx dy
 5.36: Evaluate the integrals in Exercises 34 to 36.21z121/yyz2dx dy dz
 5.37: Write the iterated integral1011x1x f (x, y, z) dz dy dxas an integr...
Solutions for Chapter 5: Double and Triple Integrals
Full solutions for Vector Calculus  6th Edition
ISBN: 9781429215084
Solutions for Chapter 5: Double and Triple Integrals
Get Full SolutionsVector Calculus was written by and is associated to the ISBN: 9781429215084. This textbook survival guide was created for the textbook: Vector Calculus, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5: Double and Triple Integrals includes 37 full stepbystep solutions. Since 37 problems in chapter 5: Double and Triple Integrals have been answered, more than 3075 students have viewed full stepbystep solutions from this chapter.

Absolute maximum
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.

Arccotangent function
See Inverse cotangent function.

Binomial coefficients
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n  r2!

Differentiable at x = a
ƒ'(a) exists

Equal complex numbers
Complex numbers whose real parts are equal and whose imaginary parts are equal.

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Imaginary part of a complex number
See Complex number.

Irrational zeros
Zeros of a function that are irrational numbers.

Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

Position vector of the point (a, b)
The vector <a,b>.

Quartile
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

Residual
The difference y1  (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

Tangent
The function y = tan x

Translation
See Horizontal translation, Vertical translation.

Tree diagram
A visualization of the Multiplication Principle of Probability.

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.