Calculate integral using rectangle method in Pascal gives 0 while in C++ good results

Question

I'm trying to implement the rectangle method in Pascal. The point is, I'm getting wrong results. I'm getting 0, while the same code in C++ gives me good results. Why is that? Thanks.

Pascal:

Program HelloWorld(output);

function degrees2radians(x: real) : real;
var
   result: real;
begin
   result := x * 3.14159 / 180.0;
end;

function fun1(x: real) : real;
var 
    result: real;
begin
    x := degrees2radians(x);
    result := Sin(x);
end;

function rect_method(a: real; b: real; n: integer) : real;
var
    result: real;
    h: real;
    integral: real;
    i : integer;
begin
    integral := 0;
    i := 0;
    h := (a - b) / n;
    for i := 1  to n do
    begin
        integral := integral + fun1(b + i*h)*h;
    end;
    result := integral;
end;

var
   result: real;

begin
  result := rect_method(1.0, -2.0, 3);
  writeln('result = ', result);
end.

And C++ (which works: https://onlinegdb.com/ubuNQInB2):

#include <iostream>
#include <cstdlib>
#include <cmath>

double degrees2radians(double x)
{
    return x * 3.14159 / 180;
}

double f1(double x)
{
    x = degrees2radians(x);
    return sin(x);
}

double rectangle_method(double a, double b, int n)
{
    float h, integral = 0;
    h = (a - b) / (double) n;

    for (int i=1; i<=n; i++)
        integral += f1(b + i*h)*h;

    return integral;
}

int main()
{
    std::cout << rectangle_method(1, -2, 3) << "\n";
    return 0;
}

Answer 1

In your Pascal code result is a local variable, which has nothing to do with the special identifier called result that you want to use:

function degrees2radians(x: real) : real;
var
   result: real;
begin
   result := x * 3.14159 / 180.0;
end;

You should remove result: real; in all your functions.

---

However, "fixed" code produces zero anyway: https://onlinegdb.com/_M2pGk134, which is actually correct. That is, this code should return zero.

I rewrote this code in Julia (the language doesn't matter, the point is that it supports high-precision floating-point types out of the box; BigFloat is such a high-precision float), and the result is still zero:

degrees2radians(x::Real)::Real = x * 3.14159 / 180

f1(x::Real) = sin(degrees2radians(x))

function rectangle_method(a::Real, b::Real, n::Integer)
    integral = 0
    h = (a - b) / n;

    for i in 1:n
      @show i f1(b + i*h)*h
      integral += f1(b + i*h)*h;
    end

    return integral;
end

@show rectangle_method(BigFloat("1"), -BigFloat("2"), 3)

The output looks like this:

i = 1
f1(b + i * h) * h = -0.01745239169736329549313317881927049082689975241899824937795751704833664190229729
i = 2
f1(b + i * h) * h = 0.0
i = 3
f1(b + i * h) * h = 0.01745239169736329549313317881927049082689975241899824937795751704833664190229729
rectangle_method(BigFloat("1"), -(BigFloat("2")), 3) = 0.0

So, f1(b + 2 * h) * h is zero, and f1(b + 1 * h) * h is exactly (look at the amount of digits after the decimal point!) the negative of f1(b + 3 * h) * h, so they cancel out in the integral sum, resulting in zero.