Order of differentiation and integration

In summary, the given identity may not be correct and the LHS needs to be determined. The identity involves a partial derivative and a double integral and it is assumed that there are no convergence issues. The specific function f(s,t) is not specified.
  • #1
toptrial
5
0
I guess the following identity isn't right. Can anyone tell me what the LHS is really equal to?
[tex]\frac{\partial}{\partial x}\int_{-\infty}^\infty\int_0^x f(s,t) dsdt = \int_{-\infty}^\infty f(x,t)dt[/tex]
 
Last edited:
Physics news on Phys.org
  • #2
toptrial said:
I guess the following identity isn't right. Can anyone tell me what the LHS is really equal to?
[tex]\frac{\partial}{\partial x}\int_{-\infty}^\infty\int_0^x f(s,t) dsdt = \int_{-\infty}^\infty f(x,t)dt[/tex]

Hi toptrial! :smile:

Looks ok to me (unless there's a convergence difficulty). :confused:

Do you have a particular f(s,t) in mind?
 

1. What is the order of differentiation and integration?

The order of differentiation and integration refers to the number of times a function is differentiated or integrated. For example, the first order of differentiation is the first derivative, while the second order is the second derivative.

2. Why is the order of differentiation and integration important?

The order of differentiation and integration is important because it affects the rate of change and the shape of a function. Higher orders of differentiation and integration can provide more precise information about the behavior of a function.

3. What is the difference between differentiation and integration?

Differentiation is the process of finding the rate of change of a function, while integration is the reverse process of finding the function itself from its derivative. In other words, differentiation is the process of finding the slope of a curve, while integration is the process of finding the area under a curve.

4. How do you find the order of differentiation or integration for a function?

The order of differentiation or integration can be determined by counting the number of times the function is differentiated or integrated. For example, if a function is differentiated twice, it is a second order derivative, while if a function is integrated three times, it is a third order integral.

5. Can the order of differentiation or integration be negative?

No, the order of differentiation or integration cannot be negative. It is always a positive integer that represents the number of times the function is differentiated or integrated.

Similar threads

I On convolution theorem of Laplace transform: Schiff
    • Calculus
Replies
4
Views
751
I Gaussian integral by differentiating under the integral sign
    • Calculus
Replies
19
Views
3K
A Multiplying divergent integrals using Hardy fields approach
    • Calculus
Replies
3
Views
1K
A Summing over continuum and uncountable numerocities
    • Calculus
Replies
1
Views
937
A Double integral with infinite limits
    • Calculus
Replies
11
Views
2K
A Is ##\delta\left(a+bi\right)=\delta\left(a-bi\right)##?
    • Calculus
Replies
3
Views
698
I On (real) entire functions and the identity theorem
    • Calculus
Replies
2
Views
790
A A discrete version of the normal distribution
    • Calculus
Replies
2
Views
1K
I Inequality with integral and max of derivative
    • Calculus
Replies
3
Views
1K
A Regarding center of mass of an infinite area
    • Calculus
Replies
5
Views
852

Hot Threads

Recent Insights

Back
Top