 8.2.1: (a) The region in Figure 8.29 is rotated around the xaxis. Using th...
 8.2.2: (a) The region in Figure 8.30 is rotated around the xaxis. Using th...
 8.2.3: (a) The region in Figure 8.31 is rotated around the yaxis. Write an...
 8.2.4: (a) The region in Figure 8.32 is rotated around the yaxis. Using th...
 8.2.5: In Exercises 514, the region is rotated around the xaxis. Find the...
 8.2.6: In Exercises 514, the region is rotated around the xaxis. Find the...
 8.2.7: In Exercises 514, the region is rotated around the xaxis. Find the...
 8.2.8: In Exercises 514, the region is rotated around the xaxis. Find the...
 8.2.9: In Exercises 514, the region is rotated around the xaxis. Find the...
 8.2.10: In Exercises 514, the region is rotated around the xaxis. Find the...
 8.2.11: In Exercises 514, the region is rotated around the xaxis. Find the...
 8.2.12: In Exercises 514, the region is rotated around the xaxis. Find the...
 8.2.13: In Exercises 514, the region is rotated around the xaxis. Find the...
 8.2.14: In Exercises 514, the region is rotated around the xaxis. Find the...
 8.2.15: For Exercises 1520, find the arc length of the graph of the functio...
 8.2.16: For Exercises 1520, find the arc length of the graph of the functio...
 8.2.17: For Exercises 1520, find the arc length of the graph of the functio...
 8.2.18: For Exercises 1520, find the arc length of the graph of the functio...
 8.2.19: For Exercises 1520, find the arc length of the graph of the functio...
 8.2.20: For Exercises 1520, find the arc length of the graph of the functio...
 8.2.21: Find the length of the parametric curves in Exercises 2124.
 8.2.22: Find the length of the parametric curves in Exercises 2124.
 8.2.23: Find the length of the parametric curves in Exercises 2124.
 8.2.24: Find the length of the parametric curves in Exercises 2124.
 8.2.25: In 2528 set up, but do not evaluate, an integral that represents th...
 8.2.26: In 2528 set up, but do not evaluate, an integral that represents th...
 8.2.27: In 2528 set up, but do not evaluate, an integral that represents th...
 8.2.28: In 2528 set up, but do not evaluate, an integral that represents th...
 8.2.29: In 2932, set up definite integral(s) to find the volume obtained wh...
 8.2.30: In 2932, set up definite integral(s) to find the volume obtained wh...
 8.2.31: In 2932, set up definite integral(s) to find the volume obtained wh...
 8.2.32: In 2932, set up definite integral(s) to find the volume obtained wh...
 8.2.33: Find the length of one arch of y = sin x
 8.2.34: Find the perimeter of the region bounded by y = x and y = x
 8.2.35: Consider the hyperbola x2 y2 = 1 in Figure 8.33. (a) The shaded reg...
 8.2.36: Rotating the ellipse x2/a2 + y2/b2 = 1 about the xaxis generates a...
 8.2.37: For 3739, sketch the solid obtained by rotating each region around ...
 8.2.38: For 3739, sketch the solid obtained by rotating each region around ...
 8.2.39: For 3739, sketch the solid obtained by rotating each region around ...
 8.2.40: The solid obtained by rotating the region around the yaxis
 8.2.41: The solid obtained by rotating the region about the xaxis.
 8.2.42: The solid obtained by rotating the region about the line y = 2.
 8.2.43: The solid whose base is the region and whose crosssections perpendi...
 8.2.44: The solid whose base is the region and whose crosssections perpendi...
 8.2.45: The solid whose base is the region and whose crosssections perpendi...
 8.2.46: The solid obtained by rotating the region about the xaxis
 8.2.47: The solid obtained by rotating the region about the horizontal line...
 8.2.48: The solid obtained by rotating the region about the horizontal line...
 8.2.49: The solid whose base is the given region and whose crosssections p...
 8.2.50: The solid whose base is the given region and whose crosssections p...
 8.2.51: Find a curve y = g(x), such that when the region between the curve ...
 8.2.52: A particle starts at the origin and moves along the curve y = 2x3/2...
 8.2.53: A tree trunk has a circular cross section at every height; its circ...
 8.2.54: Rotate the bellshaped curve y = ex2/2 shown in Figure 8.34 around ...
 8.2.55: (a) A pie dish is 9 inches across the top, 7 inches across the bott...
 8.2.56: A 100 cm long gutter is made of three strips of metal, each 5 cm wi...
 8.2.57: The design of boats is based on Archimedes Principle, which states ...
 8.2.58: The circumference of a tree at different heights above the ground i...
 8.2.59: A bowl has the shape of the graph of y = x4 between the points (1, ...
 8.2.60: The hull of a boat has widths given by the following table. Reading...
 8.2.61: (a) Write an integral which represents the circumference of a circl...
 8.2.62: Compute the perimeter of the region used for the base of the solids...
 8.2.63: Write an integral that represents the arc length of the portion of ...
 8.2.64: Find a curve y = f(x) whose arc length from x = 1 to x = 4 is given...
 8.2.65: Write a simplified expression that represents the arc length of the...
 8.2.66: Write an expression that represents the arc length of the concaved...
 8.2.67: With x and b in meters, a chain hangs in the shape of the catenary ...
 8.2.68: There are very few elementary functions y = f(x) for which arc leng...
 8.2.69: After doing 68, you may wonder what sort of functions can represent...
 8.2.70: Consider the graph of the equation x k + y k = 1, k constant. F...
 8.2.71: In 7173, explain what is wrong with the statement
 8.2.72: In 7173, explain what is wrong with the statement
 8.2.73: In 7173, explain what is wrong with the statement
 8.2.74: A region in the plane which gives the same volume whether rotated a...
 8.2.75: A region where the solid obtained by rotating the region around the...
 8.2.76: Two different curves from (0, 0) to (10, 0) that have the same arc ...
 8.2.77: A function f(x) whose graph passes through the points (0, 0) and (1...
 8.2.78: Of two solids of revolution, the one with the greater volume is obt...
 8.2.79: f f is differentiable on the interval [0, 10], then the arc length ...
 8.2.80: If f is concave up for all x and f (0) = 3/4, then the arc length o...
 8.2.81: If f is concave down for all x and f (0) = 3/4, then the arc length...
Solutions for Chapter 8.2: APPLICATIONS TO GEOMETRY
Full solutions for Calculus: Single Variable  6th Edition
ISBN: 9780470888643
Solutions for Chapter 8.2: APPLICATIONS TO GEOMETRY
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6. Chapter 8.2: APPLICATIONS TO GEOMETRY includes 81 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643. Since 81 problems in chapter 8.2: APPLICATIONS TO GEOMETRY have been answered, more than 33620 students have viewed full stepbystep solutions from this chapter.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Bar chart
A rectangular graphical display of categorical data.

Blocking
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

Components of a vector
See Component form of a vector.

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

Instantaneous rate of change
See Derivative at x = a.

Inverse composition rule
The composition of a onetoone function with its inverse results in the identity function.

Inverse cosecant function
The function y = csc1 x

Irrational numbers
Real numbers that are not rational, p. 2.

Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

Midpoint (on a number line)
For the line segment with endpoints a and b, a + b2

Negative angle
Angle generated by clockwise rotation.

Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.

Pie chart
See Circle graph.

Rational zeros
Zeros of a function that are rational numbers.

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Reference angle
See Reference triangle

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.

Weights
See Weighted mean.

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