 5.4.1: If f is an odd function, why is 1 a a f 1x2 dx = 0?
 5.4.2: If f is an even function, why is 1 a a f 1x2 dx = 21 a 0 f 1x2 dx?
 5.4.3: Is x12 an even or odd function? Is sin x2 an even or odd function?
 5.4.4: Explain how to find the average value of a function on an interval ...
 5.4.5: Explain the statement that a continuous function on an interval 3a,...
 5.4.6: Sketch the function y = x on the interval 30, 24 and let R be the r...
 5.4.7: 716. Symmetry in integrals Use symmetry to evaluate the following i...
 5.4.8: 716. Symmetry in integrals Use symmetry to evaluate the following i...
 5.4.9: 716. Symmetry in integrals Use symmetry to evaluate the following i...
 5.4.10: 716. Symmetry in integrals Use symmetry to evaluate the following i...
 5.4.11: 716. Symmetry in integrals Use symmetry to evaluate the following i...
 5.4.12: 716. Symmetry in integrals Use symmetry to evaluate the following i...
 5.4.13: 716. Symmetry in integrals Use symmetry to evaluate the following i...
 5.4.14: 716. Symmetry in integrals Use symmetry to evaluate the following i...
 5.4.15: 716. Symmetry in integrals Use symmetry to evaluate the following i...
 5.4.16: 716. Symmetry in integrals Use symmetry to evaluate the following i...
 5.4.17: 1720. Symmetry and definite integrals Use symmetry to evaluate the ...
 5.4.18: 1720. Symmetry and definite integrals Use symmetry to evaluate the ...
 5.4.19: 1720. Symmetry and definite integrals Use symmetry to evaluate the ...
 5.4.20: 1720. Symmetry and definite integrals Use symmetry to evaluate the ...
 5.4.21: 2130. Average values Find the average value of the following functi...
 5.4.22: 2130. Average values Find the average value of the following functi...
 5.4.23: 2130. Average values Find the average value of the following functi...
 5.4.24: 2130. Average values Find the average value of the following functi...
 5.4.25: 2130. Average values Find the average value of the following functi...
 5.4.26: 2130. Average values Find the average value of the following functi...
 5.4.27: 2130. Average values Find the average value of the following functi...
 5.4.28: 2130. Average values Find the average value of the following functi...
 5.4.29: 2130. Average values Find the average value of the following functi...
 5.4.30: 2130. Average values Find the average value of the following functi...
 5.4.31: Average distance on a parabola What is the average distance between...
 5.4.32: Average elevation The elevation of a path is given by f 1x2 = x3  ...
 5.4.33: Average height of an arch The height of an arch above the ground is...
 5.4.34: Average height of a wave The surface of a water wave is described b...
 5.4.35: 3540. Mean Value Theorem for Integrals Find or approximate all poin...
 5.4.36: 3540. Mean Value Theorem for Integrals Find or approximate all poin...
 5.4.37: 3540. Mean Value Theorem for Integrals Find or approximate all poin...
 5.4.38: 3540. Mean Value Theorem for Integrals Find or approximate all poin...
 5.4.39: 3540. Mean Value Theorem for Integrals Find or approximate all poin...
 5.4.40: 3540. Mean Value Theorem for Integrals Find or approximate all poin...
 5.4.41: Explain why or why not Determine whether the following statements a...
 5.4.42: 4245. Symmetry in integrals Use symmetry to evaluate the following ...
 5.4.43: 4245. Symmetry in integrals Use symmetry to evaluate the following ...
 5.4.44: 4245. Symmetry in integrals Use symmetry to evaluate the following ...
 5.4.45: 4245. Symmetry in integrals Use symmetry to evaluate the following ...
 5.4.46: Root mean square The root mean square (or RMS) is another measure o...
 5.4.47: Gateway Arch The Gateway Arch in St. Louis is 630 ft high and has a...
 5.4.48: Another Gateway Arch Another description of the Gateway Arch is y =...
 5.4.49: Planetary orbits The planets orbit the Sun in elliptical orbits wit...
 5.4.50: Comparing a sine and a quadratic function Consider the functions f ...
 5.4.51: Using symmetry Suppose f is an even function and L 8 8 f 1x2 dx = ...
 5.4.52: Using symmetry Suppose f is an odd function, L 4 0 f 1x2 dx = 3, an...
 5.4.53: 5356. Symmetry of composite functions Prove that the integrand is e...
 5.4.54: 5356. Symmetry of composite functions Prove that the integrand is e...
 5.4.55: 5356. Symmetry of composite functions Prove that the integrand is e...
 5.4.56: 5356. Symmetry of composite functions Prove that the integrand is e...
 5.4.57: Average value with a parameter Consider the function f 1x2 = ax11 ...
 5.4.58: Square of the average For what polynomials f is it true that the sq...
 5.4.59: of antiquity Several calculus problems were solved by Greek mathema...
 5.4.60: Unit area sine curve Find the value of c such that the region bound...
 5.4.61: Unit area cubic Find the value of c 7 0 such that the region bounde...
 5.4.62: Unit area a. Consider the curve y = 1>x, for x 1. For what value of...
 5.4.63: A sine integral by Riemann sums Consider the integral I = 1 p>2 0 s...
 5.4.64: Alternate definitions of means Consider the function f 1t2 = 1 b a ...
 5.4.65: Symmetry of powers Fill in the following table with either even or ...
 5.4.66: Average value of the derivative Suppose that f _ is a continuous fu...
 5.4.67: Symmetry about a point A function f is symmetric about a point 1c, ...
 5.4.68: Bounds on an integral Suppose f is continuous on 3a, b4 with f _1x2...
 5.4.69: Generalizing the Mean Value Theorem for Integrals Suppose f and g a...
Solutions for Chapter 5.4: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 5.4
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. Chapter 5.4 includes 69 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. Since 69 problems in chapter 5.4 have been answered, more than 57536 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Components of a vector
See Component form of a vector.

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

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

Logarithmic form
An equation written with logarithms instead of exponents

Mathematical model
A mathematical structure that approximates phenomena for the purpose of studying or predicting their behavior

Multiplication property of equality
If u = v and w = z, then uw = vz

Perihelion
The closest point to the Sun in a planet’s orbit.

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

Quadrant
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Real number line
A horizontal line that represents the set of real numbers.

Reciprocal of a real number
See Multiplicative inverse of a real number.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

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

Supply curve
p = ƒ(x), where x represents production and p represents price

Variable (in statistics)
A characteristic of individuals that is being identified or measured.

Velocity
A vector that specifies the motion of an object in terms of its speed and direction.

Zero vector
The vector <0,0> or <0,0,0>.