// Composite Trapezoidal Rule ---- Assignemnt 1 --- Question A
#define _USE_MATH_DEFINES
#include<stdio.h>
 
#include <cmath>
#include <iostream>
#include <fstream>
#include <cmath>
#include <tuple>
using namespace std;
// Function --- f(x) = 4/(1+x^{2})
float y(float x)
{
    // Declaring the computational function f(x) = 4/(1+x^{2})
    return 4/(1+x*x);
}
 
// Computational function to evaluate the definite Integral 
float trapezoidal(float lowlim, float uplim, float n)
{
    // Grid Spacing or Width of the Trapezoid along x-Axis
    float h = (uplim-lowlim)/n;
 
    // Calculating the f(lowlim) and f(uplim) summation
    float s = y(lowlim)+y(uplim);
 
    // Calculating the Middle Terms of the Composite Trapezoid Formula
    for (int i = 1; i < n; i++)
        s += 2*y(lowlim+i*h);
 
    // Multiplying with Grid Spacing by 2 (Sum of Parallel Sides * (Height/2))
    return (h/2)*s;
}

int main()
{
    // Range of Definite Integral
    float x0 = 0;
    float xn = 1;
    printf("PI %6.15f\n", M_PI );
    printf("\n");
 
    long long int n = 5;
    //Loop to Evaluate the Answer for Multiple Values of n
    while( n < 1000000 ){
      // Printing the Answer to a 20 Digit Precision
      printf("Value of integral is = %6.15f\n", trapezoidal(x0, xn, n));
      double e = abs(M_PI - trapezoidal(x0, xn, n));
      double loge = log(abs(M_PI - trapezoidal(x0, xn, n)));
      double logn = log(n);
      
      printf("log(n) = %6.15f\n", logn);
      printf("Error in the Intgral Computation is = %6.18f\n", e);
      printf("log(abs(error)) = %6.15f\n", loge);
      printf("\n");
      
      tuple <double, double> var;
      var = make_tuple(logn, loge);
      
      n = n*5;
      
    }
    
    return 0;
}
by

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About C++

C++ is a widely used middle-level programming language.

  • Supports different platforms like Windows, various Linux flavours, MacOS etc
  • C++ supports OOPS concepts like Inheritance, Polymorphism, Encapsulation and Abstraction.
  • Case-sensitive
  • C++ is a compiler based language
  • C++ supports structured programming language
  • C++ provides alot of inbuilt functions and also supports dynamic memory allocation.
  • Like C, C++ also allows you to play with memory using Pointers.

Syntax help

Loops

1. If-Else:

When ever you want to perform a set of operations based on a condition If-Else is used.

if(conditional-expression) {
   //code
}
else {
   //code
}

You can also use if-else for nested Ifs and If-Else-If ladder when multiple conditions are to be performed on a single variable.

2. Switch:

Switch is an alternative to If-Else-If ladder.

switch(conditional-expression){    
case value1:    
 // code    
 break;  // optional  
case value2:    
 // code    
 break;  // optional  
......    
    
default:     
 code to be executed when all the above cases are not matched;    
}

3. For:

For loop is used to iterate a set of statements based on a condition.

for(Initialization; Condition; Increment/decrement){  
  //code  
}

4. While:

While is also used to iterate a set of statements based on a condition. Usually while is preferred when number of iterations are not known in advance.

while (condition) {  
// code 
}

5. Do-While:

Do-while is also used to iterate a set of statements based on a condition. It is mostly used when you need to execute the statements atleast once.

do {  
 // code 
} while (condition);

Functions

Function is a sub-routine which contains set of statements. Usually functions are written when multiple calls are required to same set of statements which increases re-usuability and modularity. Function gets run only when it is called.

How to declare a Function:

return_type function_name(parameters);

How to call a Function:

function_name (parameters)

How to define a Function:

return_type function_name(parameters) {  
 // code
}