# Help with Double integration

• anirban84
In summary, the conversation discusses the need to do a double integration of a form involving a function and limits over two variables, as well as the use of the Runge-Kutta method for solving differential equations with initial states. The speaker also mentions the need for a feedback loop to improve initial predictions.

#### anirban84

I need to do a double integration of the form

int{ int{ f(x(t1),y(t2)) dt1 dt2 } } limit over t1 {0 : pa} and over t2 {o:pb}.

Now i have a data set for x for equal spaced t1 values varing from 0 to pa .
and for y for equal spaced t2 values varing from 0 to pb.

I will be very happy if anyone could help me ?

There may be better methods but the only way I solved differential equations with software was via the Runge-Kutta method:

http://en.wikipedia.org/wiki/Runge-Kutta

The issue here is you need an initial state, for example for ballistics, you'd need the initial position and velocity. These would be used to calcuate accelerations, and the Runge Kutta method would be used to predict a new position and velocity after a very small period of time had passed. This process is repeated until the path is "completed".

For the first few steps, some type of feedback loop is needed to make the initial predictions more accurate.

I understand the importance of accurately integrating data to analyze and understand complex systems. The double integration you have described can be a challenging task, but with the right approach, it can be achieved effectively.

Firstly, it is important to understand the concept of double integration. In this case, we are essentially integrating a function of two variables, f(x,y), over two separate intervals, t1 and t2. This can be thought of as finding the area under the surface created by the function over the two intervals.

To solve this problem, we can use the method of iterated integration. This involves first integrating the function f(x,y) with respect to t1, while treating t2 as a constant. This will give us a new function in terms of t2. Then, we can integrate this new function with respect to t2, while treating t1 as a constant. This will give us the final result of the double integration.

In your case, since you have a data set for x and y, you can use numerical methods such as the trapezoidal rule or Simpson's rule to approximate the integrals. These methods involve dividing the interval into smaller subintervals and calculating the area under the curve using the data points at the endpoints of each subinterval.

In summary, to perform the double integration described, you can use the method of iterated integration and numerical methods to approximate the integrals. It is also important to ensure that the data points for x and y are equally spaced and cover the appropriate intervals. I hope this helps and good luck with your integration!

## 1. What is Double Integration?

Double integration is a mathematical concept that involves finding the area under a two-dimensional curve. It is a fundamental tool in calculus and is used to solve problems in physics, engineering, and other scientific fields.

## 2. How is Double Integration different from Single Integration?

Single integration involves finding the area under a one-dimensional curve, while double integration involves finding the area under a two-dimensional curve. This means that double integration is more complex and requires a deeper understanding of calculus.

## 3. What are the steps to solve a Double Integration problem?

The first step is to set up the integral by identifying the limits of integration and the function to be integrated. Then, use the rules of integration to solve the integral. Finally, evaluate the integral by plugging in the limits of integration and solving for the final answer.

## 4. What are some common applications of Double Integration?

Double integration is commonly used in physics to find the total displacement, velocity, or acceleration of an object. It is also used in engineering to calculate the area of irregular shapes or to find the volume of a three-dimensional object.

## 5. What are some techniques for solving more complex Double Integration problems?

One technique is to use the properties of symmetry to simplify the problem. Another technique is to change the order of integration, which can make the integral easier to solve. Additionally, using substitution or integration by parts can also be helpful in solving more complex double integration problems.