Q. 6 Fill in the blanks to complete e... [FREE SOLUTION]

Chapter 4: Q. 6 (page 403)

Fill in the blanks to complete each of the following theorem statements:
6. The Second Fundamental Theorem of Calculus: Suppose $f$ is _____ on $[a, b]$ and, for all $x 鈭� [a, b]$ , we define
$F (x) = {鈭�}_{a}^{x} f (t) d t$ Then,
$F$ is ___ on $[a, b]$ and on $(a, b)$ , and $F$ is an _ of $f$ , or in other words, = ___ .

Short Answer

Expert verified

The Second Fundamental Theorem of Calculus: Suppose $f$ is continous on $[a, b]$ and, for all $x 鈭� [a, b]$ , we define

$F (x) = {鈭�}_{a}^{x} f (t) d t$

Then $F$ is continous on $[a, b]$ and differentiable on $(a, b)$ , and $F$ is an antiderivative of $f$ , or in other words, $F' (x) = f (x)$ .

Step by step solution

Step 1. Given data

We have to complete the statement,

The Second Fundamental Theorem of Calculus: Suppose $f$ is _____ on $[a, b]$ and, for all $x 鈭� [a, b]$ , we define

$F (x) = {鈭�}_{a}^{x} f (t) d t$

Then $F$ is _____ on $[a, b]$ and differentiable on $(a, b)$ , and $F$ is an ____ of $f$ , or in other words, ____ = _____ .

Step 2. Fill in the blanks

The Second Fundamental Theorem of Calculus: Suppose $f$ is continous on $[a, b]$ and, for all $x 鈭� [a, b]$ , we define

$F (x) = {鈭�}_{a}^{x} f (t) d t$

Then $F$ is differntiable on $[a, b]$ and antiderivative on $(a, b)$ , and $F$ is an antiderivative of $f$ , or in other words, localid="1649352465544" $F' (x) = f (x)$

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

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

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Step 1. Given data

Step 2. Fill in the blanks

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Decision Maths

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

91影视

Fill in the blanks to complete each of the following theorem statements:6. The Second Fundamental Theorem of Calculus: Suppose fis _____ on [a,b]and, for all x鈭�[a,b], we defineF(x)=鈭�axf(t)dtThen,Fis _____ on [a,b]and ____ on (a,b), and Fis an _____ of f, or in other words, ____ = _____ .

Short Answer

Step by step solution

Step 1. Given data

Step 2. Fill in the blanks

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Decision Maths

Theoretical and Mathematical Physics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.