 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 29447 students have viewed full stepbystep solutions from this chapter. Calculus: Single Variable was written by and is associated to the ISBN: 9780470888643.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Associative properties
a + (b + c) = (a + b) + c, a(bc) = (ab)c.

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

Control
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable

Convergence of a sequence
A sequence {an} converges to a if limn: q an = a

De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)

Difference of complex numbers
(a + bi)  (c + di) = (a  c) + (b  d)i

Halfplane
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

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)

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

Parametrization
A set of parametric equations for a curve.

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Resolving a vector
Finding the horizontal and vertical components of a vector.

Secant line of ƒ
A line joining two points of the graph of ƒ.

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Terminal side of an angle
See Angle.

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.