 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 8682 students have viewed full stepbystep solutions from this chapter. Calculus: Single Variable was written by Patricia and is associated to the ISBN: 9780470888643.

Arccosecant function
See Inverse cosecant function.

Axis of symmetry
See Line of symmetry.

Base
See Exponential function, Logarithmic function, nth power of a.

Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2  x 1, y2  y19>

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Multiplicative inverse of a matrix
See Inverse of a matrix

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

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Polar form of a complex number
See Trigonometric form of a complex number.

Polynomial interpolation
The process of fitting a polynomial of degree n to (n + 1) points.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Range screen
See Viewing window.

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

Real zeros
Zeros of a function that are real numbers.

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

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Scientific notation
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

Subtraction
a  b = a + (b)
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