Q. 13 - Calculus

Question

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible 

13. The formal definition of the natural logarithm function in terms of an accumulation integral

Step-by-Step Solution

Answer

The natural logarithm function is the function that for $x > 0$ is defined by

$\ln x={\int }_1^x\frac{1}{t}dt$

Step 1. Given information

We have to write the formal definition of the natural logarithm function in terms of an accumulation integral 

Step 2. Definition

The natural logarithm function is the function that for $x > 0$ is defined by 

$\ln x={\int }_1^x\frac{1}{t}dt$