Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

Answers without the blur.

Just sign up for free and you're in.

Short Answer

q

The summary of the material for the topic "Area Accumulation". is:

Differentiating a composition involving an area accumulation function.
Properties of the natural logarithm function.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The area accumulation functions
The second fundamental theorem of calculus
Differentiating a composition involving an area accumulation function
Properties of the natural logarithm function

Step 2. Explanation

If function $f$ is continuous on the interval [a,b].

The signed area between the graph of $f$ and the $x -$ axis is given by the definite integral $\int_{a}^{b} f (x) d x$ is equal to the area accumulation function.

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

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

Properties of the natural logarithm function:

$\ln (x)$ is continuous on $(0, \infty)$

$\ln (x)$ is differentiable on $(0, \infty)$

$\frac{d (\ln (x)}{d x} = \frac{1}{x} \ln (1) = 0 \ln (x) < 0 o n (0, 1) \ln (x) > 0 o n (1, \infty) \ln (x) i s i n c r e a \sin g o n (0, \infty) \ln (x) i s c o n c a v e d o w n o n (0, \infty)$

Find Study Materials for

Create Study Materials

Select your language

Calculus

Answers without the blur.

Short Answer

q

Step by Step Solution

Step 1. Given Information.

Step 2. Explanation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Calculus

Answers without the blur.

Short Answer

q

Step by Step Solution

Step 1. Given Information.

Step 2. Explanation

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Calculus

Pure Maths