Explanation Given information: f ( x ) = 2 ; a = 0 , b = 1 . Explanation: The average value of a continuous function f ( x ) over the interval a ≤ x ≤ b is defined as the quantity 1 b − a ∫ a b f ( x ) d x . Here, f ( x ) = 2 and 0 ≤ x ≤ 1 Also, f ( x ) = 2 is a continuous function. Therefore, the average value of a continuous function f ( x ) = 2 over the interval 0 ≤ x ≤ 1 is given by 1 1 − 0 ∫ 0 1 2 d x

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

See similar textbooks

Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Videos

Question

Chapter 6.5, Problem 4E

To determine

The average value of f(x)=2 over the interval from x=a to x=b where a=0, b=1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.5, Problem 3E

Chapter 6.5, Problem 5E

Students have asked these similar questions

Consider the function f(x) = x²-1. (a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative. Show all your steps clearly. (b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the graph where x 1 and x-> 1+h (for a small positive value of h, illustrate conceptually). Then, draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the value you found in part (a). (c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in the context of the graph of f(x). How does the rate of change of this function vary at different points?

1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist, state that fact. и (a) f'(-5) (b) f'(-3) (c) f'(0) (d) f'(5) 2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5) = 4. - 3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2) and f'(2).

Does the series converge or diverge

Chapter 6 Solutions

Calculus & Its Applications (14th Edition)

Ch. 6.1 - Determine the following: a. t7/2dt b....Ch. 6.1 - Find a function f(t) that satisfies f(t)=3t+5 and...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Find all antiderivatives of each following...Ch. 6.1 - Determine the following: 4x3dx Ch. 6.1 - Determine the following: 13xdx

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The average value of f ( x ) = 2 over the interval from x = a to x = b where a = 0 , b = 1 .

Solution Summary: The author explains that the average value of a continuous function f(x)=2 is 2.

Concept explainers

Videos

The average value of f(x)=2 over the interval from x=a to x=b where a=0, b=1.

Want to see the full answer?

Chapter 6 Solutions