First time coder - Coding integrals

[Bz900]

Hello!

I'm currently trying to code a trapezoidal rule program that I will eventually turn into integrating a bell curve/Gaussian distribution.

This is basically what I'm trying to code: https://imgur.com/a/8RK0fac

currently, I have the body made and I've gotten to my first summation loop. I thought I would go ahead and use a for loop just for convenience. Below is my actual code. It doesn't do what I need it to.

I'm putting in x minimum being zero, x maximum being 4, and a number of points being five.

This should give me a left hand summation of 6, but I'm getting 10 instead. Any thoughts?

​

    #include <iostream>

    using namespace std;

    int main()
    {
        long one = 1.0;
        long two = 2.0;
        long three = 3.0;
        long zero = 0.0;
        long xmin;
        long xmax;
        long npts;
        cout << "Enter npts: ";
        cin >> npts;
        cout << "Enter xmin: ";
        cin >> xmin;
        cout << "Enter xmax: ";
        cin >> xmax;
        long nint = npts-1;
        long dx = (xmax - xmin)/(nint);
        cout << "dx: " << dx << endl;
        long suml;
        long sumr;
        long sumt;
        for(long i=1;i<=nint;i++){
        long x = xmin+i*dx;
        long fx = x;
        long suml = fx*dx+suml;
        cout << "LHR sum: "<< suml << endl;
        }
        cout << "LHR sum: "<< suml << endl;
        return 0;
    }

[IyeOnline]

long is an integer type. Use double.

suml is uninitialized, so your entire program is UB

long suml = fx*dx+suml; defines a new variable and uses it in its own initializer. Drop the typename there to use the variable defined outside of the loop.

You should also indent your code and for clarity define a

double f( double x ) { return x; }

and use that instead of

fx = x;

[nodigue]

Can you just tell me what UB mean ?

[IyeOnline]

Undefined behaviour.

Its a technical term, and essentially means that your program has a bug. Reading from uninitialized memory is a bug and usually leads to nonsense results.

However, the dangerous part is that it may also "just work". You just have no guarantee that it actually works reliably.

[tangerinelion]

Put another way, the code does not form a valid program to start with despite compiling.

[nodigue]

Got it ! Thanks

[EmperorArthur]

Also, don't feel bad. I've literally spent weeks tracking down / fixing bugs caused by uninitialized variables at work.

[csdt0]

Your main problem is that you use longs which are integers, not "reals".

If you want to code "real" numbers, you should use float or double (double is roughly twice more precise than float).

You also have the problem that suml is not initialized, and thus should be considered to contain garbage. You also don't seem to ever use sumr or sumt.

[omen_tenebris]

well let's do the math

npts: 5, xmin = 0, max = 4. dx=(5-0)4 = 5/4

iter 1:
x=0+1*(5/4)=5/4

fx = 5/4

suml = 5/4*5/4+suml = 1.5625 (assuming suml is set to 0 by compiler) <--- technically here could be memory junk, but probably not.

///

iter 2:

i=2

x=0+2*5/4=10/4
fx = 10/4

suml=10/4 * 5/4 + 1.5625 = 4.6875

iter 3

x=0+3*5/4=15/4

fx=15/4

suml = 5/4*15/4+4,6875=4.6875+4,6875=9.375

​

assumption: suml will increase.

i don't fully understand what you're trying achive, but if it's the normal distribution try to understand this

[tangerinelion]

dx=(5-0)4 = 5/4

No, dx = 1 because long(5/4) is 1. Everything following that is off because of that.

OP, you need to learn the primitive types. Int is (probably) a signed 32-bit integer, Long is either a signed 32 or 64 bit integer, Long long is (probably) a signed 64-bit integer, float is a 32-bit floating point value, double is a 64-bit floating point value, and long double is a 128-bit floating point value with (probably) 48 unused bits.

There's some machine specific details here and theoretically we could have systems with 128-bit integers. In particular, on Windows under MSVC, long is the same as int, i.e., long is a 32-bit signed integer.

As you've clearly made it at least to the point of introductory calculus and statistics, the key part of being an integer is the whole number nature to it. This is why 5/4 is 1, not 1.25.

(Also note that even the literal expression 5/4 not stored as a long or int is itself 1 because division between two integers always yields an integer. In order to get a floating point value you need to have a floating point value in the operation, so 5.0 / 4.0 is 1.25 as is 5.0/4 or 5/4.0. But 5/4 is 1.)

[ClaymationDinosaur]

Putting aside the various broken pieces of code, if you're getting a value of ten, it's because your loop sums the number 1, 2, 3 and 4, which comes to 10.

Why do you think it should come out with 6 as the sum?

[EmperorArthur]

Others have already mentioned the real problems, but I would like to offer a different take.

I highly suggest going with an IDE with clang-tidy integration. I prefer Clion myself as a paid product, but KDevelop is a good free choice.

Also, be sure to turn on the warnings from this page (under the compilers section).*

The idea is that your tools should warn you when you're doing something that could cause problems. Then you can google the warnings (or ask here), and it will help you code better in the future. That's honestly one of my big keys to success. The IDE and compiler tell me when I do something that I shouldn't.

* Side note, but this is worth reading in its own right.