Why Does ∫ln(x) dx Include dx?

In summary, the integral of ln x is the natural logarithm of x and is important in calculus and various scientific and engineering applications. It can be found using integration by parts, substitution, or other methods. The domain of the integral is all positive real numbers except 0. Real-world applications include population growth, medicine dosage, and radioactive decay analysis.
  • #1
markosheehan
136
0
find ∫ln x dx. i can't work this out but i know its integration. why is there a dx here. there is usually no dx when i am differentiating something
 
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  • #2
markosheehan said:
find ∫ln x dx. i can't work this out but i know its integration. why is there a dx here. there is usually no dx when i am differentiating something

All integrals are written with dx at the end, it's read as "the integral of the function ln(x) with respect to x".

And all derivatives have the same, have you never noticed that "dx" in dy/dx?
 

FAQ: Why Does ∫ln(x) dx Include dx?

What is the integral of ln x?

The integral of ln x is the natural logarithm of x. It represents the area under the curve of the function ln x from 1 to x.

Why is the integral of ln x important?

The integral of ln x is important because it is a fundamental concept in calculus and is used to solve a variety of mathematical problems. It is also used in many scientific and engineering applications.

How do you find the integral of ln x?

To find the integral of ln x, you can use integration by parts or substitution. The result will be ln x times the value of x minus the integral of 1/x. You can also use a table of integrals or a graphing calculator to find the integral.

What is the domain of the integral of ln x?

The domain of the integral of ln x is all positive real numbers, excluding 0.

What are some real-world applications of the integral of ln x?

The integral of ln x has many real-world applications, including calculating the growth rate of populations, determining the amount of medicine in a person's body over time, and analyzing the decay of radioactive substances.

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