ind the average value of the function over the glven Interval and all values of x In the Interval for which the fundtion equals Its average value. (x) = 4x - 3x, [-2, 4]

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...
icon
Related questions
Question
Please solve for step 3, disregard the answers in the boxes: all steps for step 3 should be solved ( all boxes), thanks!!!
Tutorial Exercise
Find the average value of the function over the glven Interval and all values of x In the Interval for which the function equals Its average value.
f(x) = 4x-3x,. (-2, 4]
Step 1
Recall that the average value of a function (x) over an Interval [a, b] Is glven by
1
f(x) dx.
b - a
Here, f(x) = 4x
and b =
-2
Step 2
Substitute the values of f(x), a, and b In the Integral from the prevlous step, and find the average value of the glven function f(x).
dx =
4- (-2)
4
Step 3
Apply the Fundamental Theorem of Calculus, which states that,
m dx = F(b) - Flo).
Apply the limits on the right side of the equation obtained in the previous step to evaluate the definite Integral.
- 64) - (64
168
6.
28
Transcribed Image Text:Tutorial Exercise Find the average value of the function over the glven Interval and all values of x In the Interval for which the function equals Its average value. f(x) = 4x-3x,. (-2, 4] Step 1 Recall that the average value of a function (x) over an Interval [a, b] Is glven by 1 f(x) dx. b - a Here, f(x) = 4x and b = -2 Step 2 Substitute the values of f(x), a, and b In the Integral from the prevlous step, and find the average value of the glven function f(x). dx = 4- (-2) 4 Step 3 Apply the Fundamental Theorem of Calculus, which states that, m dx = F(b) - Flo). Apply the limits on the right side of the equation obtained in the previous step to evaluate the definite Integral. - 64) - (64 168 6. 28
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning