Chapter 4: Q. 8 (page 403)

Fill in the blanks to complete each of the following theorem statements:
8. If $f$ is on $[a, b]$ and $u (x)$ is on $[a, b]$ , then for all $x \in [a, b]$ ,
$\frac{d}{d x} \int_{a}^{u (x)} f (t) d t =____$

Short Answer

Expert verified

If $f$ is on $[a, b]$ and $u (x)$ is on $[a, b]$ , then for all $x \in [a, b]$

\frac{d}{d x} \int_{a}^{u (x)} f (t) d t = f (u (x)) u' (x)

Step by step solution

Step 1. Given information

We have to complete the statement,

If $f$ is on $[a, b]$ and $u (x)$ is on $[a, b]$ , then for all $x \in [a, b]$ ,

\frac{d}{d x} \int_{a}^{u (x)} f (t) d t =____

Step 2. Fill in the blanks

If $f$ is on $[a, b]$ and $u (x)$ is on $[a, b]$ , then for all $x \in [a, b]$ ,

\frac{d}{d x} \int_{a}^{u (x)} f (t) d t = f (u (x)) u' (x)

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Fill in the blanks to complete each of the following theorem statements:
8. If $f$ is on $[a, b]$ and $u (x)$ is on $[a, b]$ , then for all $x \in [a, b]$ ,
$\frac{d}{d x} \int_{a}^{u (x)} f (t) d t =____$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Fill in the blanks

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Fill in the blanks to complete each of the following theorem statements:8. If fis on [a,b]and u(x)is on [a,b], then for all x∈[a,b], ddx∫au(x)f(t)dt=____

Short Answer

Step by step solution

Step 1. Given information

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

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Fill in the blanks to complete each of the following theorem statements:
8. If $f$ is on $[a, b]$ and $u (x)$ is on $[a, b]$ , then for all $x \in [a, b]$ ,
$\frac{d}{d x} \int_{a}^{u (x)} f (t) d t =____$