 6.3.1: Let be the solid obtained by rotating the region shown in the figur...
 6.3.2: Let be the solid obtained by rotating the region shown in the figur...
 6.3.3: Use the method of cylindrical shells to find the volume generated b...
 6.3.4: Use the method of cylindrical shells to find the volume generated b...
 6.3.5: Use the method of cylindrical shells to find the volume generated b...
 6.3.6: Use the method of cylindrical shells to find the volume generated b...
 6.3.7: Use the method of cylindrical shells to find the volume generated b...
 6.3.8: Let be the volume of the solid obtained by rotating about the axis...
 6.3.9: Use the method of cylindrical shells to find the volume of the soli...
 6.3.10: Use the method of cylindrical shells to find the volume of the soli...
 6.3.11: Use the method of cylindrical shells to find the volume of the soli...
 6.3.12: Use the method of cylindrical shells to find the volume of the soli...
 6.3.13: Use the method of cylindrical shells to find the volume of the soli...
 6.3.14: Use the method of cylindrical shells to find the volume of the soli...
 6.3.15: Use the method of cylindrical shells to find the volume generated b...
 6.3.16: Use the method of cylindrical shells to find the volume generated b...
 6.3.17: Use the method of cylindrical shells to find the volume generated b...
 6.3.18: Use the method of cylindrical shells to find the volume generated b...
 6.3.19: Use the method of cylindrical shells to find the volume generated b...
 6.3.20: Use the method of cylindrical shells to find the volume generated b...
 6.3.21: Set up, but do not evaluate, an integral for the volume of the soli...
 6.3.22: Set up, but do not evaluate, an integral for the volume of the soli...
 6.3.23: Set up, but do not evaluate, an integral for the volume of the soli...
 6.3.24: Set up, but do not evaluate, an integral for the volume of the soli...
 6.3.25: Set up, but do not evaluate, an integral for the volume of the soli...
 6.3.26: Set up, but do not evaluate, an integral for the volume of the soli...
 6.3.27: Use the Midpoint Rule with to estimate the volume obtained by rotat...
 6.3.28: If the region shown in the figure is rotated about the axis to for...
 6.3.29: Each integral represents the volume of a solid. Describe the solid.
 6.3.30: Each integral represents the volume of a solid. Describe the solid.
 6.3.31: Each integral represents the volume of a solid. Describe the solid.
 6.3.32: Each integral represents the volume of a solid. Describe the solid.
 6.3.33: Use a graph to estimate the coordinates of the points of intersect...
 6.3.34: Use a graph to estimate the coordinates of the points of intersect...
 6.3.35: Use a computer algebra system to find the exact volume of the solid...
 6.3.36: Use a computer algebra system to find the exact volume of the solid...
 6.3.37: The region bounded by the given curves is rotated about the specifi...
 6.3.38: The region bounded by the given curves is rotated about the specifi...
 6.3.39: The region bounded by the given curves is rotated about the specifi...
 6.3.40: The region bounded by the given curves is rotated about the specifi...
 6.3.41: The region bounded by the given curves is rotated about the specifi...
 6.3.42: The region bounded by the given curves is rotated about the specifi...
 6.3.43: Use cylindrical shells to find the volume of the solid.
 6.3.44: Use cylindrical shells to find the volume of the solid.
 6.3.45: Use cylindrical shells to find the volume of the solid.
 6.3.46: Suppose you make napkin rings by drilling holes with different diam...
Solutions for Chapter 6.3: Volumes by Cylindrical Shells
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 6.3: Volumes by Cylindrical Shells
Get Full SolutionsChapter 6.3: Volumes by Cylindrical Shells includes 46 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus,, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Since 46 problems in chapter 6.3: Volumes by Cylindrical Shells have been answered, more than 46661 students have viewed full stepbystep solutions from this chapter. Calculus, was written by and is associated to the ISBN: 9780534393397.

Backtoback stemplot
A stemplot with leaves on either side used to compare two distributions.

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Horizontal Line Test
A test for determining whether the inverse of a relation is a function.

Index
See Radical.

Instantaneous rate of change
See Derivative at x = a.

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Mapping
A function viewed as a mapping of the elements of the domain onto the elements of the range

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

Negative numbers
Real numbers shown to the left of the origin on a number line.

Partial sums
See Sequence of partial sums.

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Random variable
A function that assigns realnumber values to the outcomes in a sample space.

Root of a number
See Principal nth root.

Sequence of partial sums
The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

Slopeintercept form (of a line)
y = mx + b

Solve by substitution
Method for solving systems of linear equations.

System
A set of equations or inequalities.

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

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.

yintercept
A point that lies on both the graph and the yaxis.