Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
Prove the Mean Value Theorem for Integrals by applying the Mean Value Theorem for derivatives (see Section 4.2) to the function $ F(x) = \displaystyle \int_{a}^x f(t) dt $.
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Amrita Bhasin
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 2 / BC
Chapter 6
Applications of Integration
Section 5
Average Value of a Function
Oregon State University
Harvey Mudd College
University of Michigan - Ann Arbor
Idaho State University
Lectures
01:06
Prove the Mean Value Theor…
04:03
06:20
02:39
Prove the Mean-Value Theor…
okay, The mean value. Their first off we know efforts continuously closed. Interval A to B and F is also different. Chewable on the open interval. A deadbeat. Therefore, we know there's a number seeing a comma be such that the derivative of prime F C is F A B minus F of a over B minus A. Therefore, we can write this out as half primacy is F A B minus off of a over B minus. And remember the fundamental theme of calculus. It means that we can essentially break up into girls like this. I remember when the integral is from a This means it's just zero, which means we can disregard it. In this case, bring us back to FC is one over B minus eight times the integral from A to B after vax d x. Thus we have now proven the mean value the arm
View More Answers From This Book
Find Another Textbook
03:15
The graph y f"'(c) of the the_derivative o a function f(1) is &…
01:31
(1 point) Consider the function belowf(c) = I+5nsFollow the step…
01:41
Determine the following by using an appropriate Riemann sum. [12 22 + 32 n2]…
01:01
The area of the rectangle depicting a uniform distribution is always equal t…
04:11
The correlation of coefficient is r =Round to 4 decimal places:
01:35
7_ A sample of size of 600 persons selected at random from large city shows …
02:14
Packaging You wish to construct closed rectangular box that has volume of 4 …
00:57
Identify the correct null and alternative hypothesesA waste management s…
05:23
point) The fourth degree Taylor polynomial for f(x) = x centered at a = -2 i…
