 7.9.1: What are T1 and T2 for a function on [0, 2] such that f (0) = 3, f ...
 7.9.2: For which graph in Figure 15 will TN overestimate the integral? Wha...
 7.9.3: How large is the error when the Trapezoidal Rule is applied to a li...
 7.9.4: What is the maximum possible error if T4 is used to approximate 3 0...
 7.9.5: What are the two graphical interpretations of the Midpoint Rule?
 7.9.6: In Exercises 112, calculate MN and TN for the value of N indicated....
 7.9.7: In Exercises 112, calculate MN and TN for the value of N indicated....
 7.9.8: In Exercises 112, calculate MN and TN for the value of N indicated....
 7.9.9: In Exercises 112, calculate MN and TN for the value of N indicated....
 7.9.10: In Exercises 112, calculate MN and TN for the value of N indicated....
 7.9.11: In Exercises 112, calculate MN and TN for the value of N indicated....
 7.9.12: In Exercises 112, calculate MN and TN for the value of N indicated....
 7.9.13: In Exercises 1322, calculate SN given by Simpsons Rule for the valu...
 7.9.14: In Exercises 1322, calculate SN given by Simpsons Rule for the valu...
 7.9.15: In Exercises 1322, calculate SN given by Simpsons Rule for the valu...
 7.9.16: In Exercises 1322, calculate SN given by Simpsons Rule for the valu...
 7.9.17: In Exercises 1322, calculate SN given by Simpsons Rule for the valu...
 7.9.18: In Exercises 1322, calculate SN given by Simpsons Rule for the valu...
 7.9.19: In Exercises 1322, calculate SN given by Simpsons Rule for the valu...
 7.9.20: In Exercises 1322, calculate SN given by Simpsons Rule for the valu...
 7.9.21: In Exercises 1322, calculate SN given by Simpsons Rule for the valu...
 7.9.22: In Exercises 1322, calculate SN given by Simpsons Rule for the valu...
 7.9.23: In Exercises 2326, calculate the approximation to the volume of the...
 7.9.24: In Exercises 2326, calculate the approximation to the volume of the...
 7.9.25: In Exercises 2326, calculate the approximation to the volume of the...
 7.9.26: In Exercises 2326, calculate the approximation to the volume of the...
 7.9.27: An airplanes velocity is recorded at 5minute (min) intervals durin...
 7.9.28: Use Simpsons Rule to determine the average temperature in a museum ...
 7.9.29: Tsunami Arrival Times Scientists estimate the arrival times of tsun...
 7.9.30: Use S8 to estimate /2 0 sin x x dx, taking the value of sin x x at ...
 7.9.31: Calculate T6 for the integral I = 2 0 x3 dx. (a) Is T6 too large or...
 7.9.32: Calculate M4 for the integral I = 1 0 x sin(x2)dx. (a) Use a plot o...
 7.9.33: In Exercises 3336, state whether TN or MN underestimates or overest...
 7.9.34: In Exercises 3336, state whether TN or MN underestimates or overest...
 7.9.35: In Exercises 3336, state whether TN or MN underestimates or overest...
 7.9.36: In Exercises 3336, state whether TN or MN underestimates or overest...
 7.9.37: In Exercises 3740, use the error bound to find a value of N for whi...
 7.9.38: In Exercises 3740, use the error bound to find a value of N for whi...
 7.9.39: In Exercises 3740, use the error bound to find a value of N for whi...
 7.9.40: In Exercises 3740, use the error bound to find a value of N for whi...
 7.9.41: Compute the error bound for the approximations T10 and M10 to 3 0 (...
 7.9.42: (a) Compute S6 for the integral I = 1 0 e2x dx. (b) Show that K4 = ...
 7.9.43: Calculate S8 for 5 1 ln xdx and calculate the error bound. Then fin...
 7.9.44: Find a bound for the error in the approximation S10 to 3 0 ex2 dx (...
 7.9.45: Use a computer algebra system to compute and graph f (4) for f (x) ...
 7.9.46: Use a computer algebra system to compute and graph f (4) for f (x) ...
 7.9.47: In Exercises 4750, use the error bound to find a value of N for whi...
 7.9.48: In Exercises 4750, use the error bound to find a value of N for whi...
 7.9.49: In Exercises 4750, use the error bound to find a value of N for whi...
 7.9.50: In Exercises 4750, use the error bound to find a value of N for whi...
 7.9.51: Show that 1 0 dx 1 + x2 = 4 [use Eq. (3) in Section 5.8]. (a) Use a...
 7.9.52: Let J = 0 ex2 dx and JN = N 0 ex2 dx. Although ex2 has no elementar...
 7.9.53: Let J = 0 ex2 dx and JN = N 0 ex2 dx. Although ex2 has no elementar...
 7.9.54: The error bound for MN is proportional to 1/N2, so the error bound ...
 7.9.55: Observe that the error bound for TN (which has 12 in the denominato...
 7.9.56: Explain why the error bound for SN decreases by 1 16 if N is increa...
 7.9.57: Verify that S2 yields the exact value of 1 0 (x x3)dx. 5
 7.9.58: Verify that S2 yields the exact value of b a (x x3)dx for all a
 7.9.59: Show that if f (x) = rx + s is a linear function (r, s constants), ...
 7.9.60: Show that if f (x) = px2 + qx + r is a quadratic polynomial, then S...
 7.9.61: For N even, divide [a,b] into N subintervals of width x = b a N . S...
 7.9.62: Show that S2 also gives the exact value for b a x3 dx and conclude,...
 7.9.63: Use the error bound for SN to obtain another proof that Simpsons Ru...
 7.9.64: Sometimes Simpsons Rule Performs Poorly Calculate M10 and S10 for t...
Solutions for Chapter 7.9: Numerical Integration
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 7.9: Numerical Integration
Get Full SolutionsCalculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7.9: Numerical Integration includes 64 full stepbystep solutions. Since 64 problems in chapter 7.9: Numerical Integration have been answered, more than 40720 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3.

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

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)

Divisor of a polynomial
See Division algorithm for polynomials.

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

Independent variable
Variable representing the domain value of a function (usually x).

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Irrational numbers
Real numbers that are not rational, p. 2.

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

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

Ordinary annuity
An annuity in which deposits are made at the same time interest is posted.

Permutations of n objects taken r at a time
There are nPr = n!1n  r2! such permutations

Positive linear correlation
See Linear correlation.

Product of functions
(ƒg)(x) = ƒ(x)g(x)

Range (in statistics)
The difference between the greatest and least values in a data set.

Root of an equation
A solution.

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

Transformation
A function that maps real numbers to real numbers.

Trigonometric form of a complex number
r(cos ? + i sin ?)

Unbounded interval
An interval that extends to ? or ? (or both).

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.