 16.7.1: Let be the cube with vertices . Approximate xy dS by using a Rieman...
 16.7.2: A surface consists of the cylinder , , together with its top and bo...
 16.7.3: Let be the hemisphere , and suppose is a continuous function with ,...
 16.7.4: Suppose that , where is a function of one variable such that . Eval...
 16.7.5: Evaluate the surface integral.
 16.7.6: Evaluate the surface integral.
 16.7.7: Evaluate the surface integral.
 16.7.8: Evaluate the surface integral.
 16.7.9: Evaluate the surface integral.
 16.7.10: Evaluate the surface integral.
 16.7.11: Evaluate the surface integral.
 16.7.12: Evaluate the surface integral.
 16.7.13: Evaluate the surface integral.
 16.7.14: Evaluate the surface integral.
 16.7.15: Evaluate the surface integral.
 16.7.16: Evaluate the surface integral.
 16.7.17: Evaluate the surface integral.
 16.7.18: Evaluate the surface integral.
 16.7.19: Evaluate the surface integral for the given vector field and the or...
 16.7.20: Evaluate the surface integral for the given vector field and the or...
 16.7.21: Evaluate the surface integral for the given vector field and the or...
 16.7.22: Evaluate the surface integral for the given vector field and the or...
 16.7.23: Evaluate the surface integral for the given vector field and the or...
 16.7.24: Evaluate the surface integral for the given vector field and the or...
 16.7.25: Evaluate the surface integral for the given vector field and the or...
 16.7.26: Evaluate the surface integral for the given vector field and the or...
 16.7.27: Evaluate the surface integral for the given vector field and the or...
 16.7.28: Evaluate the surface integral for the given vector field and the or...
 16.7.29: Evaluate correct to four decimal places, where is the surface ,
 16.7.30: Find the exact value of , where is the surface in Exercise 29.
 16.7.31: Find the value of correct to four decimal places, where is the part...
 16.7.32: Find the flux of across the part of the cylinder that lies above th...
 16.7.33: Find a formula for similar to Formula 8 for the case where is given...
 16.7.34: Find a formula for similar to Formula 8 for the case where is given...
 16.7.35: Find the center of mass of the hemisphere , , if it has constant de...
 16.7.36: Find the mass of a thin funnel in the shape of a cone , , if its de...
 16.7.37: (a) Give an integral expression for the moment of inertia about the...
 16.7.38: The conical surface , , has constant density . Find (a) the center ...
 16.7.39: A fluid with density 1200 flows with velocity . Find the rate of fl...
 16.7.40: A fluid has density 1500 and velocity field . Find the rate of flow...
 16.7.41: Use Gausss Law to find the charge contained in the solid hemisphere...
 16.7.42: Use Gausss Law to find the charge enclosed by the cube with vertice...
 16.7.43: The temperature at the point in a substance with conductivity is . ...
 16.7.44: The temperature at a point in a ball with conductivity is inversely...
Solutions for Chapter 16.7: Surface Integrals
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 16.7: Surface Integrals
Get Full SolutionsSince 44 problems in chapter 16.7: Surface Integrals have been answered, more than 43721 students have viewed full stepbystep solutions from this chapter. Calculus, was written by and is associated to the ISBN: 9780534393397. This textbook survival guide was created for the textbook: Calculus,, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 16.7: Surface Integrals includes 44 full stepbystep solutions.

Components of a vector
See Component form of a vector.

Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Difference of two vectors
<u1, u2>  <v1, v2> = <u1  v1, u2  v2> or <u1, u2, u3>  <v1, v2, v3> = <u1  v1, u2  v2, u3  v3>

equation of a quadratic function
ƒ(x) = ax 2 + bx + c(a ? 0)

Event
A subset of a sample space.

Fundamental
Theorem of Algebra A polynomial function of degree has n complex zeros (counting multiplicity).

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Instantaneous velocity
The instantaneous rate of change of a position function with respect to time, p. 737.

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Linear inequality in two variables x and y
An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Negative angle
Angle generated by clockwise rotation.

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

Positive linear correlation
See Linear correlation.

Row operations
See Elementary row operations.

Symmetric property of equality
If a = b, then b = a

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

Whole numbers
The numbers 0, 1, 2, 3, ... .

Ymax
The yvalue of the top of the viewing window.