 5.4.1: In Exercises 16, find the integral, given that  b a f(x) dx = 8, ...
 5.4.2: In Exercises 16, find the integral, given that  b a f(x) dx = 8, ...
 5.4.3: In Exercises 16, find the integral, given that  b a f(x) dx = 8, ...
 5.4.4: In Exercises 16, find the integral, given that  b a f(x) dx = 8, ...
 5.4.5: In Exercises 16, find the integral, given that  b a f(x) dx = 8, ...
 5.4.6: In Exercises 16, find the integral, given that  b a f(x) dx = 8, ...
 5.4.7: In Exercises 710, find the average value of the function over the g...
 5.4.8: In Exercises 710, find the average value of the function over the g...
 5.4.9: In Exercises 710, find the average value of the function over the g...
 5.4.10: In Exercises 710, find the average value of the function over the g...
 5.4.11: (a) Using Figure 5.66, find  6 1 f(x) dx. (b) What is the average ...
 5.4.12: How do the units for the average value of f relate to the units for...
 5.4.13: Find the area of the regions in Exercises 1320
 5.4.14: Find the area of the regions in Exercises 1320
 5.4.15: Find the area of the regions in Exercises 1320
 5.4.16: Find the area of the regions in Exercises 1320
 5.4.17: Find the area of the regions in Exercises 1320
 5.4.18: Find the area of the regions in Exercises 1320
 5.4.19: Find the area of the regions in Exercises 1320
 5.4.20: Find the area of the regions in Exercises 1320
 5.4.21: (a) Let  3 0 f(x)dx = 6. What is the average value of f(x) on the ...
 5.4.22: Using Figure 5.67, write  3 0 f(x) dx in terms of  1 1 f(x) dx an...
 5.4.23: (a) Assume a b. Use geometry to construct a formula in terms of a a...
 5.4.24: If  5 2 (2f(x) + 3) dx = 17, find  5 2 f(x) dx
 5.4.25: The value, V , of a Tiffany lamp, worth $225 in 1975, increases at ...
 5.4.26: (a) Assume that 0 a b. Use geometry to construct a formula in terms...
 5.4.27: If f(x) is odd and  3 2 f(x) dx = 30, find  3 2 f(x) dx.
 5.4.28: If f(x) is even and  2 2(f(x) 3) dx = 8, find  2 0 f(x) dx.
 5.4.29: Without any computation, find , /4 /4 x3 cos x2 dx.
 5.4.30: If the average value of f on the interval 2 x 5 is 4, find  5 2 (3...
 5.4.31: Suppose  3 1 3x2 dx = 26 and  3 1 2x dx = 8. What is  3 1 (x2 x)...
 5.4.32: Figure 5.68 shows the rate, f(x), in thousands of algae per hour, a...
 5.4.33: (a) Using Figure 5.69, estimate  3 3 f(x) dx. (b) Which of the fol...
 5.4.34: A bar of metal is cooling from 1000C to room temperature, 20C. The ...
 5.4.35: In 2010, the population of Mexico8 was growing at 1.1% a year. Assu...
 5.4.36: (a) Using a graph, decide if the area under y = ex2/2 between 0 and...
 5.4.37: Without computation, show that 2 , 2 0 1 + x3 dx 6.
 5.4.38: Without calculating the integral, explain why the following stateme...
 5.4.39: For 3942, mark the quantity on a copy of the graph of f in Figure 5...
 5.4.40: For 3942, mark the quantity on a copy of the graph of f in Figure 5...
 5.4.41: For 3942, mark the quantity on a copy of the graph of f in Figure 5...
 5.4.42: For 3942, mark the quantity on a copy of the graph of f in Figure 5...
 5.4.43: Using the graph of f in Figure 5.71, arrange the following quantiti...
 5.4.44: (a) Using Figures 5.72 and 5.73, find the average value on 0 x 2 of...
 5.4.45: (a) Without computing any integrals, explain why the average value ...
 5.4.46: Figure 5.74 shows the standard normal distribution from statistics,...
 5.4.47: Figure 5.74 shows the standard normal distribution from statistics,...
 5.4.48: Figure 5.74 shows the standard normal distribution from statistics,...
 5.4.49: In 4952, evaluate the expression if possible, or say what extra inf...
 5.4.50: In 4952, evaluate the expression if possible, or say what extra inf...
 5.4.51: In 4952, evaluate the expression if possible, or say what extra inf...
 5.4.52: In 4952, evaluate the expression if possible, or say what extra inf...
 5.4.53: (a) Sketch a graph of f(x) = sin(x2) and mark on it the points x = ...
 5.4.54: For 5456, assuming F = f, mark the quantity on a copy of Figure 5.75.
 5.4.55: For 5456, assuming F = f, mark the quantity on a copy of Figure 5.75.
 5.4.56: For 5456, assuming F = f, mark the quantity on a copy of Figure 5.75.
 5.4.57: In Chapter 2, the average velocity over the time interval a t b was...
 5.4.58: In 5860, explain what is wrong with the statemen
 5.4.59: In 5860, explain what is wrong with the statemen
 5.4.60: In 5860, explain what is wrong with the statemen
 5.4.61: In 6163, give an example of:
 5.4.62: In 6163, give an example of:
 5.4.63: In 6163, give an example of:
 5.4.64: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.65: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.66: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.67: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.68: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.69: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.70: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.71: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.72: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.73: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.74: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.75: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.76: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.77: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.78: In 6478, are the statements true for all continuous functions f(x) ...
 5.4.79: Which of the following statements follow directly from the rule , b...
Solutions for Chapter 5.4: THEOREMS ABOUT DEFINITE INTEGRALS 2
Full solutions for Calculus: Single Variable  6th Edition
ISBN: 9780470888643
Solutions for Chapter 5.4: THEOREMS ABOUT DEFINITE INTEGRALS 2
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Single Variable , edition: 6. Chapter 5.4: THEOREMS ABOUT DEFINITE INTEGRALS 2 includes 79 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 79 problems in chapter 5.4: THEOREMS ABOUT DEFINITE INTEGRALS 2 have been answered, more than 34790 students have viewed full stepbystep solutions from this chapter. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Circular functions
Trigonometric functions when applied to real numbers are circular functions

Constraints
See Linear programming problem.

Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian threedimensional space

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

Division
a b = aa 1 b b, b Z 0

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Jump discontinuity at x a
limx:a  ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

Octants
The eight regions of space determined by the coordinate planes.

Ordered set
A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

Range screen
See Viewing window.

Reflection
Two points that are symmetric with respect to a lineor a point.

Slant asymptote
An end behavior asymptote that is a slant line

Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Stem
The initial digit or digits of a number in a stemplot.

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.