For each function f and interval [a, b] in Exercises 56–67, use definite integrals and the Fundamental Theorem of Calculus to find the exact average value of f from x = a to x = b. Then use a graph of f to verify that your answer is reasonable. 56. f() — х — 1, [-1,3] 57. f(x) = 3x + 1, [0, 4] 58. f(x) = 4 – x², [-2, 2] 59. f(x) = 4, [-37.2, 103.75] 60. f(x) = (x + 2)² – 5, [–5,0] 61. f) %3 х2 — 2х - 1, [0,3] 62. f(x) = 4x3/2, [a, b] = [0, 2] 63. f(x) = (e*)², [a, b] = [=1, 1] 1 64. f(x) = [a, b] = [2, 5] Зх + 1' 65. f(x) = 2 – VI, [a, b] = [1,8] 66. f(x) = x² sin(x³ + 1), [a, b] = [-1,2] 67. f(x) = sinx+x cos x, [a, b] = [-1,7] %3D
For each function f and interval [a, b] in Exercises 56–67, use definite integrals and the Fundamental Theorem of Calculus to find the exact average value of f from x = a to x = b. Then use a graph of f to verify that your answer is reasonable. 56. f() — х — 1, [-1,3] 57. f(x) = 3x + 1, [0, 4] 58. f(x) = 4 – x², [-2, 2] 59. f(x) = 4, [-37.2, 103.75] 60. f(x) = (x + 2)² – 5, [–5,0] 61. f) %3 х2 — 2х - 1, [0,3] 62. f(x) = 4x3/2, [a, b] = [0, 2] 63. f(x) = (e*)², [a, b] = [=1, 1] 1 64. f(x) = [a, b] = [2, 5] Зх + 1' 65. f(x) = 2 – VI, [a, b] = [1,8] 66. f(x) = x² sin(x³ + 1), [a, b] = [-1,2] 67. f(x) = sinx+x cos x, [a, b] = [-1,7] %3D
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![For each function f and interval [a, b] in Exercises 56–67, use
definite integrals and the Fundamental Theorem of Calculus
to find the exact average value of f from x = a to x = b. Then
use a graph of f to verify that your answer is reasonable.
56. f() — х — 1, [-1,3]
57. f(x) = 3x + 1, [0, 4]
58. f(x) = 4 – x², [-2, 2]
59. f(x) = 4, [-37.2, 103.75]
60. f(x) = (x + 2)² – 5, [–5,0]
61. f) %3 х2 — 2х - 1, [0,3]
62. f(x) = 4x3/2, [a, b] = [0, 2]
63. f(x) = (e*)², [a, b] = [=1, 1]
1
64. f(x) =
[a, b] = [2, 5]
Зх + 1'
65. f(x) = 2 – VI, [a, b] = [1,8]
66. f(x) = x² sin(x³ + 1), [a, b] = [-1,2]
67. f(x) = sinx+x cos x,
[a, b] = [-1,7]
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa86966be-df6f-471c-a9dd-7b11ab02e9da%2F152050f5-ec27-4a50-808b-06362dff4cbb%2Fpi1wl1m_processed.png&w=3840&q=75)
Transcribed Image Text:For each function f and interval [a, b] in Exercises 56–67, use
definite integrals and the Fundamental Theorem of Calculus
to find the exact average value of f from x = a to x = b. Then
use a graph of f to verify that your answer is reasonable.
56. f() — х — 1, [-1,3]
57. f(x) = 3x + 1, [0, 4]
58. f(x) = 4 – x², [-2, 2]
59. f(x) = 4, [-37.2, 103.75]
60. f(x) = (x + 2)² – 5, [–5,0]
61. f) %3 х2 — 2х - 1, [0,3]
62. f(x) = 4x3/2, [a, b] = [0, 2]
63. f(x) = (e*)², [a, b] = [=1, 1]
1
64. f(x) =
[a, b] = [2, 5]
Зх + 1'
65. f(x) = 2 – VI, [a, b] = [1,8]
66. f(x) = x² sin(x³ + 1), [a, b] = [-1,2]
67. f(x) = sinx+x cos x,
[a, b] = [-1,7]
%3D
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