Having problems implementing mathematical equations in programming

Question

I am implementing an algorithm for school and am having problems understanding how a definite integral is represented in programming. For example I know that the Summation equation can be implemented as the following example:

assuming y=f(x)

if(x==0){
    y=x+1;
}else{
    for(int i = 0; i < n; i++){
        y = y + (x - 1);
    }
}

How would I then represent a numerical integral, example:

The equations planted here may not make mathematical sense but my objective is to implement similar equations in c# for a school programming project that I have to do in which I have to implement an algorithm which contains integrals. I have been reading that there are numerical methods to solve definite integrals such as simpson rule; would I have to use such methods to implement the equation or can an integral be represented in programming such as a loop or something of that sort?

Answer 1

It depends on what you are trying to do. If this was a specific implementation you could simply integrate the formula x-1 becomes (x^2)/2 - x and then return the max value minus the minimum value.

Alternatively it can be implemented as an estimation choosing an appropriate step size for dx.

decimal dx=0.1;

if(x==0){  
    y=x+1;  // could just return y=1
}else{  
    decimal tempY=0;
    for(decimal i = 3; i <= 20; i+=dx){  
        tempY += (i - 1);  
    }  
    // Either return tempY as decimal or
    y= Convert.ToInt32(tempY);
}