Write a program to calculate double integral numerically.
Input: Given the following integral. where Output: 3.915905
Explanation and Approach:
- We need to decide what method we are going to use to solve the integral.
In this example, we are going to use Simpson 1/3 method for both x and y integration.
To do so, first, we need to decide the step size. Let h be the step size for integration with respect to x and k be the step size for integration with respect to y.
We are taking h=0.1 and k=0.15 in this example.
Refer for Simpson 1/3 rule
- We need to create a table which consists of the value of function f(x, y) for all possible combination of all x and y points.
x\y y0 y1 y2 …. ym x0 f(x0, y0) f(x0, y1) f(x0, y2) …. f(x0, ym) x1 f(x1, y0) f(x1, y1) f(x1, y2) …. f(x1, ym) x2 f(x2, y0) f(x2, y1) f(x2, y2) …. f(x2, ym) x3 f(x3, y0) f(x3, y1) f(x3, y2) …. f(x3, ym) …. …. …. …. …. …. …. …. …. …. …. …. xn f(xn, y0) f(xn, y1) f(xn, y2) …. f(xn, ym)
In the given problem,
x0=2.3 x2=2.4 x3=3.5 y0=3.7 y1=3.85 y2=4 y3=4.15 y4=4.3
- After generating the table, we apply Simpson 1/3 rule (or whatever rule is asked in the problem) on each row of the table to find integral wrt y at each x and store the values in an array ax.
- We again apply Simpson 1/3 rule(or whatever rule asked) on the values of array ax to calculate the integral wrt x.
Below is the implementation of the above code:
- Program to calculate Profit Or Loss
- Program to calculate distance between two points in 3 D
- Program to calculate the area between two Concentric Circles
- Program to calculate the Surface Area of a Triangular Prism
- Program to calculate area of an Circle inscribed in a Square
- Program to calculate the number of odd days in given number of years
- C Program to Add two Integers
- Program to find greater value between a^n and b^n
- Program to check if two strings are same or not
- Writing first C++ program : Hello World example
- Program to find the number of men initially
- Program to Print Alphabets from A to Z Using Loop
- C Program to Check Whether a Number is Prime or not
- Program to find Nth term of series 9, 23, 45, 75, 113...
- Program to find Nth term of the series 2, 4, 3, 4, 15...
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.