 6.3.1: Suppose a cut is made through a solid object perpendicular to the x...
 6.3.2: A solid has a circular base and cross sections perpendicular to the...
 6.3.3: The region bounded by the curves y = 2x and y = x2 is revolved abou...
 6.3.4: The region bounded by the curves y = 2x and y = x2 is revolved abou...
 6.3.5: Why is the disk method a special case of the general slicing method?
 6.3.6: The region R bounded by the graph of y = f 1x2 0 and the xaxis on ...
 6.3.7: 716. General slicing method Use the general slicing method to find ...
 6.3.8: 716. General slicing method Use the general slicing method to find ...
 6.3.9: 716. General slicing method Use the general slicing method to find ...
 6.3.10: 716. General slicing method Use the general slicing method to find ...
 6.3.11: 716. General slicing method Use the general slicing method to find ...
 6.3.12: 716. General slicing method Use the general slicing method to find ...
 6.3.13: 716. General slicing method Use the general slicing method to find ...
 6.3.14: 716. General slicing method Use the general slicing method to find ...
 6.3.15: 716. General slicing method Use the general slicing method to find ...
 6.3.16: 716. General slicing method Use the general slicing method to find ...
 6.3.17: 1726. Disk method Let R be the region bounded by the following curv...
 6.3.18: 1726. Disk method Let R be the region bounded by the following curv...
 6.3.19: 1726. Disk method Let R be the region bounded by the following curv...
 6.3.20: 1726. Disk method Let R be the region bounded by the following curv...
 6.3.21: 1726. Disk method Let R be the region bounded by the following curv...
 6.3.22: 1726. Disk method Let R be the region bounded by the following curv...
 6.3.23: 1726. Disk method Let R be the region bounded by the following curv...
 6.3.24: 1726. Disk method Let R be the region bounded by the following curv...
 6.3.25: 1726. Disk method Let R be the region bounded by the following curv...
 6.3.26: 1726. Disk method Let R be the region bounded by the following curv...
 6.3.27: 2734. Washer method Let R be the region bounded by the following cu...
 6.3.28: 2734. Washer method Let R be the region bounded by the following cu...
 6.3.29: 2734. Washer method Let R be the region bounded by the following cu...
 6.3.30: 2734. Washer method Let R be the region bounded by the following cu...
 6.3.31: 2734. Washer method Let R be the region bounded by the following cu...
 6.3.32: 2734. Washer method Let R be the region bounded by the following cu...
 6.3.33: 2734. Washer method Let R be the region bounded by the following cu...
 6.3.34: 2734. Washer method Let R be the region bounded by the following cu...
 6.3.35: 3540. Disks , washers about the yaxis Let R be the region bounded ...
 6.3.36: 3540. Disks , washers about the yaxis Let R be the region bounded ...
 6.3.37: 3540. Disks , washers about the yaxis Let R be the region bounded ...
 6.3.38: 3540. Disks , washers about the yaxis Let R be the region bounded ...
 6.3.39: 3540. Disks , washers about the yaxis Let R be the region bounded ...
 6.3.40: 3540. Disks , washers about the yaxis Let R be the region bounded ...
 6.3.41: 4144. Which is greater? For the following regions R, determine whic...
 6.3.42: 4144. Which is greater? For the following regions R, determine whic...
 6.3.43: 4144. Which is greater? For the following regions R, determine whic...
 6.3.44: 4144. Which is greater? For the following regions R, determine whic...
 6.3.45: The region R bounded by the graphs of x = 0, y = 1x, and y = 1 is r...
 6.3.46: The region R bounded by the graphs of x = 0, y = 1x, and y = 2 is r...
 6.3.47: The region R bounded by the graph of y = 2 sin x and the xaxis on ...
 6.3.48: The region R bounded by the graph of y = ln x and the yaxis on the...
 6.3.49: The region R bounded by the graphs of y = sin x and y = 1  sin x o...
 6.3.50: The region R in the first quadrant bounded by the graphs of y = x a...
 6.3.51: The region R in the first quadrant bounded by the graphs of y = 2 ...
 6.3.52: The region R is bounded by the graph of f 1x2 = 2x12  x2 and the x...
 6.3.53: Explain why or why not Determine whether the following statements a...
 6.3.54: The region bounded by y = 1ln x2>1x, y = 0, and x = 2 revolved abou...
 6.3.55: The region bounded by y = 1>1x, y = 0, x = 2, and x = 6 revolved ab...
 6.3.56: The region bounded by y = 1 3x2 + 1 and y = 1 12 revolved about the...
 6.3.57: The region bounded by y = ex, y = 0, x = 0, and x = 2 revolved abou...
 6.3.58: The region bounded by y = ex, y = ex, x = 0, and x = ln 4 revolved...
 6.3.59: The region bounded by y = ln x, y = ln x2, and y = ln 8 revolved ab...
 6.3.60: The region bounded by y = ex, y = 0, x = 0, and x = p 7 0 revolved...
 6.3.61: Fermats volume calculation ( ) Let R be the region bounded by the c...
 6.3.62: Solid from a piecewise function Let f 1x2 = c x if 0 x 2 2x  2 if ...
 6.3.63: Solids from integrals Sketch a solid of revolution whose volume by ...
 6.3.64: Volume of a wooden object A solid wooden object turned on a lathe h...
 6.3.65: Cylinder, cone, hemisphere A right circular cylinder with height R ...
 6.3.66: Water in a bowl A hemispherical bowl of radius 8 inches is filled t...
 6.3.67: A torus (doughnut) Find the volume of the torus formed when the cir...
 6.3.68: Which is greater? Let R be the region bounded by y = x2 and y = 1x....
 6.3.69: Cavalieris principle Cavalieris principle states that if two solids...
 6.3.70: Limiting volume Consider the region R in the first quadrant bounded...
Solutions for Chapter 6.3: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 6.3
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. Since 70 problems in chapter 6.3 have been answered, more than 54166 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 6.3 includes 70 full stepbystep solutions.

Central angle
An angle whose vertex is the center of a circle

Circle
A set of points in a plane equally distant from a fixed point called the center

Components of a vector
See Component form of a vector.

Direction of an arrow
The angle the arrow makes with the positive xaxis

Equivalent arrows
Arrows that have the same magnitude and direction.

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Inverse function
The inverse relation of a onetoone function.

Line of symmetry
A line over which a graph is the mirror image of itself

Maximum rvalue
The value of r at the point on the graph of a polar equation that has the maximum distance from the pole

Natural logarithm
A logarithm with base e.

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Rectangular coordinate system
See Cartesian coordinate system.

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Seconddegree equation in two variables
Ax 2 + Bxy + Cy2 + Dx + Ey + F = 0, where A, B, and C are not all zero.

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Tangent
The function y = tan x