Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Q. 5 (page 372)

What important theorem is the key to proving the Fundamental Theorem of Calculus?

Short Answer

Expert verified

The key to proving the Fundamental Theorem of Calculus is the Mean Value Theorem.

Step by step solution

01

Step 1. Given Information.

We have to find the objective which is the key to proving the Fundamental Theorem of Calculus.

02

Step 2. The theorem.

The key to proving the Fundamental Theorem of Calculus is the Mean Value Theorem.

The Mean Value Theorem is applied to anti-derivatives. It allows for relating the average rate of change of anti-derivatives to the instantaneous rate of change or the derivative of the anti-derivative.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Explain why the formula for the integral of xkdoes not

apply whenk=-1. What is the integral of x-1?

Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating.

∫3x2+1dx

Calculate the exact value of each definite integral in Exercises 47–52 by using properties of definite integrals and the formulas in Theorem 4.13.

∫04(2x-3)2+5dx

Determine which of the limit of sums in Exercises 47–52 are infinite and which are finite. For each limit of sums that is finite, compute its value

limn→∞∑k=1nk+12n3-1

Find the sum or quantity without completely expanding or calculating any sums.

Given∑k=025k=325and∑k=328k-32=14,910, find the value of∑k=325k2-5k+9.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free