 6.2.1: What is the average value of f on [0, 4] if the area between the gr...
 6.2.2: Find the volume of a solid extending from y = 2 to y = 5 if every c...
 6.2.3: What is the definition of flow rate?
 6.2.4: Which assumption about fluid velocity did we use to compute the flo...
 6.2.5: The average value of f on [1, 4] is 5. Find 4 1 f (x) dx.
 6.2.6: Find the volume of the wedge in Figure 20(A) by integrating the are...
 6.2.7: Derive a formula for the volume of the wedge in Figure 20(B) in ter...
 6.2.8: Let B be the solid whose base is the unit circle x2 + y2 = 1 and wh...
 6.2.9: In Exercises 914, find the volume of the solid with the given base ...
 6.2.10: The base is the triangle enclosed by x + y = 1, the xaxis, and the...
 6.2.11: The base is the semicircle y = 9 x2, where 3 x 3. The cross section...
 6.2.12: The base is a square, one of whose sides is the interval [0, ] alon...
 6.2.13: The base is the region enclosed by y = x2 and y = 3. The cross sect...
 6.2.14: The base is the region enclosed by y = x2 and y = 3. The cross sect...
 6.2.15: Find the volume of the solid whose base is the region x+y 1 and...
 6.2.16: Show that a pyramid of height h whose base is an equilateral triang...
 6.2.17: The area of an ellipse is ab, where a and b are the lengths of the ...
 6.2.18: Find the volume V of a regular tetrahedron (Figure 22) whose face i...
 6.2.19: A frustum of a pyramid is a pyramid with its top cut off [Figure 23...
 6.2.20: A plane inclined at an angle of 45 passes through a diameter of the...
 6.2.21: The solid S in Figure 25 is the intersection of two cylinders of ra...
 6.2.22: Let S be the intersection of two cylinders of radius r whose axes i...
 6.2.23: Calculate the volume of a cylinder inclined at an angle = 30 with h...
 6.2.24: The areas of cross sections of Lake Nogebow at 5m intervals are gi...
 6.2.25: Find the total mass of a 1m rod whose linear density function is (...
 6.2.26: Find the total mass of a 2m rod whose linear density function is (...
 6.2.27: A mineral deposit along a strip of length 6 cm has density s(x) = 0...
 6.2.28: Charge is distributed along a glass tube of length 10 cm with linea...
 6.2.29: Calculate the population within a 10mile radius of the city center...
 6.2.30: Odzala National Park in the Republic of the Congo has a high densit...
 6.2.31: Table 1 lists the population density (in people per square kilomete...
 6.2.32: Find the total mass of a circular plate of radius 20 cm whose mass ...
 6.2.33: The density of deer in a forest is the radial function (r) = 150(r2...
 6.2.34: Show that a circular plate of radius 2 cm with radial mass density ...
 6.2.35: Find the flow rate through a tube of radius 4 cm, assuming that the...
 6.2.36: The velocity of fluid particles flowing through a tube of radius 5 ...
 6.2.37: A solid rod of radius 1 cm is placed in a pipe of radius 3 cm so th...
 6.2.38: Let v(r) be the velocity of blood in an arterial capillary of radiu...
 6.2.39: In Exercises 3948, calculate the average over the given interval. 3...
 6.2.40: In Exercises 3948, calculate the average over the given interval.f ...
 6.2.41: In Exercises 3948, calculate the average over the given interval.f ...
 6.2.42: In Exercises 3948, calculate the average over the given interval.f ...
 6.2.43: In Exercises 3948, calculate the average over the given interval.f ...
 6.2.44: In Exercises 3948, calculate the average over the given interval.f ...
 6.2.45: In Exercises 3948, calculate the average over the given interval.f ...
 6.2.46: In Exercises 3948, calculate the average over the given interval.f ...
 6.2.47: In Exercises 3948, calculate the average over the given interval.f ...
 6.2.48: In Exercises 3948, calculate the average over the given interval.f ...
 6.2.49: The temperature (in degrees Celsius) at time t (in hours) in an art...
 6.2.50: A steel bar of length 3 m experiences extreme heat at its center, s...
 6.2.51: Temperature in the town of Walla Walla during the month of July fol...
 6.2.52: The door to the garage is left open and over the next 4 hours (h), ...
 6.2.53: A 10cm copper wire with one end in an ice bath is heated at the ot...
 6.2.54: A ball thrown in the air vertically from ground level with initial ...
 6.2.55: Find the average speed over the time interval [1, 5] (time in secon...
 6.2.56: An object with zero initial velocity accelerates at a constant rate...
 6.2.57: The acceleration of a particle is a(t) = 60t 4t3 m/s2. Compute the ...
 6.2.58: What is the average area of the circles whose radii vary from 0 to R?
 6.2.59: Let M be the average value of f (x) = x4 on [0, 3]. Find a value of...
 6.2.60: Let f (x) = x. Find a value of c in [4, 9] such that f (c) is equal...
 6.2.61: Let M be the average value of f (x) = x3 on [0, A], where A > 0. Wh...
 6.2.62: Let M be the average value of f (x) = x3 on [0, A], where A > 0. Wh...
 6.2.63: Which of f (x) = x sin2 x and g(x) = x2 sin2 x has a larger average...
 6.2.64: Find the average of f (x) = ax + b over the interval [M,M], where a...
 6.2.65: Sketch the graph of a function f such that f (x) 0 on [0, 1] and f ...
 6.2.66: Give an example of a function (necessarily discontinuous) that does...
 6.2.67: An object is tossed into the air vertically from ground level with ...
 6.2.68: Review the MVT stated in Section 4.3 (Theorem 1, p. 226) and show h...
Solutions for Chapter 6.2: Setting Up Integrals: Volume, Density, Average Value
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 6.2: Setting Up Integrals: Volume, Density, Average Value
Get Full SolutionsSince 68 problems in chapter 6.2: Setting Up Integrals: Volume, Density, Average Value have been answered, more than 44367 students have viewed full stepbystep solutions from this chapter. Chapter 6.2: Setting Up Integrals: Volume, Density, Average Value includes 68 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885.

Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.

Arcsine function
See Inverse sine function.

Center
The central point in a circle, ellipse, hyperbola, or sphere

Coefficient
The real number multiplied by the variable(s) in a polynomial term

Conditional probability
The probability of an event A given that an event B has already occurred

Dependent event
An event whose probability depends on another event already occurring

Irrational zeros
Zeros of a function that are irrational numbers.

Logistic regression
A procedure for fitting a logistic curve to a set of data

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Negative angle
Angle generated by clockwise rotation.

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Onetoone rule of exponents
x = y if and only if bx = by.

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

Ordered pair
A pair of real numbers (x, y), p. 12.

Partial fraction decomposition
See Partial fractions.

Quartic function
A degree 4 polynomial function.

Quartile
The first quartile is the median of the lower half of a set of data, the second quartile is the median, and the third quartile is the median of the upper half of the data.

Real number
Any number that can be written as a decimal.

Subtraction
a  b = a + (b)

xcoordinate
The directed distance from the yaxis yzplane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.