 8.2.1: 1 4 (a) Set up an integral for the area of the surface obtained by ...
 8.2.2: 1 4 (a) Set up an integral for the area of the surface obtained by ...
 8.2.3: 1 4 (a) Set up an integral for the area of the surface obtained by ...
 8.2.4: 1 4 (a) Set up an integral for the area of the surface obtained by ...
 8.2.5: 512 Find the exact area of the surface obtained by rotating the cur...
 8.2.6: 512 Find the exact area of the surface obtained by rotating the cur...
 8.2.7: 512 Find the exact area of the surface obtained by rotating the cur...
 8.2.8: 512 Find the exact area of the surface obtained by rotating the cur...
 8.2.9: 512 Find the exact area of the surface obtained by rotating the cur...
 8.2.10: 512 Find the exact area of the surface obtained by rotating the cur...
 8.2.11: 512 Find the exact area of the surface obtained by rotating the cur...
 8.2.12: 512 Find the exact area of the surface obtained by rotating the cur...
 8.2.13: 1316 The given curve is rotated about the axis. Find the area of t...
 8.2.14: 1316 The given curve is rotated about the axis. Find the area of t...
 8.2.15: 1316 The given curve is rotated about the axis. Find the area of t...
 8.2.16: 1316 The given curve is rotated about the axis. Find the area of t...
 8.2.17: 1720 Use Simpsons Rule with to approximate the area of the surface ...
 8.2.18: 1720 Use Simpsons Rule with to approximate the area of the surface ...
 8.2.19: 1720 Use Simpsons Rule with to approximate the area of the surface ...
 8.2.20: 1720 Use Simpsons Rule with to approximate the area of the surface ...
 8.2.21: 2122 Use either a CAS or a table of integrals to find the exact are...
 8.2.22: 2122 Use either a CAS or a table of integrals to find the exact are...
 8.2.23: 2324 Use a CAS to find the exact area of the surface obtained by ro...
 8.2.24: 2324 Use a CAS to find the exact area of the surface obtained by ro...
 8.2.25: If the region is rotated about the axis, the volume of the resulti...
 8.2.26: If the infinite curve , , is rotated about the axis, find the area...
 8.2.27: (a) If , find the area of the surface generated by rotating the loo...
 8.2.28: A group of engineers is building a parabolic satellite dish whose s...
 8.2.29: (a) The ellipse is rotated about the axis to form a surface called...
 8.2.30: Find the surface area of the torus in Exercise 61 in Section 6.2.
 8.2.31: If the curve , , is rotated about the horizontal line , where , fin...
 8.2.32: Use the result of Exercise 31 to set up an integral to find the are...
 8.2.33: Find the area of the surface obtained by rotating the circle about ...
 8.2.34: (a) Show that the surface area of a zone of a sphere that lies betw...
 8.2.35: Formula 4 is valid only when . Show that when is not necessarily po...
 8.2.36: Let be the length of the curve , , where is positive and has a cont...
Solutions for Chapter 8.2: Area of a Surface of Revolution
Full solutions for Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
Solutions for Chapter 8.2: Area of a Surface of Revolution
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 36 problems in chapter 8.2: Area of a Surface of Revolution have been answered, more than 31318 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. Chapter 8.2: Area of a Surface of Revolution includes 36 full stepbystep solutions.

Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Constant of variation
See Power function.

Conversion factor
A ratio equal to 1, used for unit conversion

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

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

Equivalent arrows
Arrows that have the same magnitude and direction.

Frequency distribution
See Frequency table.

Horizontal component
See Component form of a vector.

Initial value of a function
ƒ 0.

Local extremum
A local maximum or a local minimum

Major axis
The line segment through the foci of an ellipse with endpoints on the ellipse

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

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Parameter interval
See Parametric equations.

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

Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.

Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc  ad c2 + d2 i

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Vertical stretch or shrink
See Stretch, Shrink.