C++ area under a curve for equation F(X) = 5x^3 + 7x^2 -3x+4; from 2 to 7 until

Question

C++ area under a curve

for equation

F(X) = 5x^3 + 7x^2 -3x+4;

from 2 to 7

until the difference between the last two calculations is less than .0001

Why does code output 3707.66 instead of the correct 3715.42?

// Source File: test.cpp
// Description: calculating the area under the curve

#include <iostream>
#include <cmath>
#include <math.h> //pow

using namespace std;

int main(){
double A = 0;
double B = 0;
double Area = 0;
double height =0;
double width = 0;
double current_total = 0;
double previous_total =0;

  
A = 2;
B = 7;
double n =10;
double xpos = 0;
double diff=1;
double prev_width = 0;
double prev_n =0;
  
do{
  
//current total

width = (B - A)/n;

for(double i =0; i < n; i++){
// F(X) = 5x^3 + 7x^2 -3x+4;
  

xpos = A + width*i+ width/2;
height = 5*pow(xpos, 3) + 7* pow(xpos, 2) - 3*xpos + 4;

Area = height * width;

  
current_total = Area + current_total;

}

//previous total   
prev_width = (B - A)/(n-1);
prev_n = n-1;

for(double i =0; i < prev_n; i++){
// F(X) = 5x^3 + 7x^2 -3x+4;
  

xpos = A + prev_width*i+ prev_width/2;
height = 5*pow(xpos, 3) + 7* pow(xpos, 2) - 3*xpos + 4;

Area = height * prev_width;

  
previous_total = Area + previous_total;

}

  
diff = current_total - previous_total ;
n++;   
  
  
  
}while ( diff < 0.0001);
cout << "Result: " << current_total << endl;
  
  
  

return 0;
}

Explanation / Answer

#include using namespace std; double f(double x); int main() { double a; double b; int n; double h; double x; double area; a = 2; b = 7; n = 10000; h = (b-a)/n; area = (f(a)+f(b))/2; for (int i=1;i

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