Program to calculate Double Integration

Write a program to calculate double integral numerically.

Example:

Input: Given the following integral.
whereOutput: 3.915905

Explanation and Approach:

1. 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
2. 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.

1. 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

1. 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[].
2. 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: 

3.915905