Integral of a partial derivative.

In summary, the integral of a partial derivative is a mathematical operation used to find the area under a curve of a function with respect to one of its variables, while the other variables are held constant. Its purpose is to analyze the behavior of multivariable functions, and it is calculated using integration techniques such as the fundamental theorem of calculus. It has various real-world applications in fields such as physics, engineering, economics, and statistics.
  • #1
Mento
1
0
Hi! :smile:

I have the following integral

[itex]\int^{∞}_{∞} \frac{\delta^{n}}{\delta a}f(a,b,c)da[/itex]

there is any way to rewrite it in terms of:

[itex]\int^{∞}_{∞} f(a,b,c)da[/itex]

I want to evaluate it for the case of n=1,2 and 3.

Thanks you so much.
 
Physics news on Phys.org
  • #2
An integral of a derivative is the function itself. I am confused as to what you want.
 

1. What is the definition of an integral of a partial derivative?

The integral of a partial derivative is a mathematical operation that involves finding the area under a curve of a function with respect to one of its variables, while keeping all other variables constant. It is represented by the symbol ∫.

2. What is the purpose of finding the integral of a partial derivative?

The purpose of finding the integral of a partial derivative is to determine how one variable affects the overall behavior of a multivariable function. It allows us to analyze the rate of change of a function with respect to a particular variable and make predictions about its behavior.

3. What is the difference between a partial derivative and an integral of a partial derivative?

A partial derivative calculates the rate of change of a multivariable function with respect to one of its variables, while keeping all other variables constant. On the other hand, the integral of a partial derivative calculates the area under the curve of a function with respect to that same variable.

4. How is the integral of a partial derivative calculated?

The integral of a partial derivative is calculated using integration techniques such as the fundamental theorem of calculus, substitution, or integration by parts. It involves finding an antiderivative of the function with respect to the variable of interest and evaluating it at the upper and lower bounds of the integration.

5. What are some real-world applications of the integral of a partial derivative?

The integral of a partial derivative has numerous real-world applications, such as in physics, engineering, economics, and statistics. It is used to calculate the velocity and acceleration of moving objects, determine optimal solutions in optimization problems, and analyze the relationship between multiple variables in various fields of study.

Similar threads

Replies
1
Views
812
Replies
4
Views
262
Replies
31
Views
750
Replies
1
Views
94
Replies
4
Views
3K
Replies
6
Views
1K
Replies
3
Views
1K
Replies
16
Views
2K
  • Calculus
Replies
1
Views
939
Back
Top