Numerical Integration with Trapezoidal rule c++ - c++

Question

I'm attempting to implement a Trapezoidal rule that utilizes previous function evaluations in order to avoid redundant computation. Two things: a) computed results are not converging and I'm a little unsure of why. I'll post of the mathematics behind why I think that the algorithm should yield convergence if it's wanted, and b) the do while loop is terminating at n=8 and I've been unable to figure that one out as well; it should be running until n>128? (n is the number of subintervals) My code is below. Thanks in advance!
void NestedTrap(int n) //Trapezoidal with reuse of function evaluations
{
double a,b; //interval end points
double x[n+1]; //equally spaced nodes
double c[n]; //midpoints
double T; //Initial integral evaluation
double T2; //Evaluation with reuse of previous function evaluations
double h, h2; //step sizes for T and T2
double temp1, temp2;
std::cout <<"Enter interval end points (lesser first; enter 999 for pi & 999.2 for pi/2 & 999.4 for pi/4): ";
std::cin >> a >> b;
if (b == 999)
{
b = M_PI;
}
if (a == 999)
{
a = M_PI;
}
if (b == 999.4)
{
b = M_PI/4;
}
if (a == 999.4)
{
a = M_PI/4;
}
if (b == 999.2)
{
b = M_PI/2;
}
if (a == 999.2)
{
a = M_PI/2;
}
h = (b-a)/n;
T = 0;
temp1 = 0;
temp2 = 0;
for (int i=0; i<=n; i++)
{
x[i] = 0;
}
for (int i=0; i<n; i++)
{
x[i+1] = x[i] + h;
}
for (int i=1; i<n; i++)
{
temp1 += I1(x[i]);
}
T = (h/2)*exp(x[0]) + (h/2)*exp(x[n]) + (h*temp1);
std::cout << "T_" << n <<": " << T << std::endl;
do
{
temp2 = 0;
n = 2*n;
h2 = (b-a)/(n);
for (int i=0; i<n; i++)
{
c[i] = 0;
}
for (int i=1; i<=n; i++)
{
c[i] = a + h2*(i-0.5);
//std::cout << c[i] << std::endl;
}
for (int i=0; i<n; i++)
{
temp2 += exp(c[i]);
}
T2 = (T/2) + h2*temp2;
std::cout << "T_" << n <<": " << T2 << std::endl;
T = T2;
} while (n <= 128);
}

Answer 1

You create arrays of size n here
double x[n+1]; //equally spaced nodes
double c[n]; //midpoints
(note that this is not valid c++)
then you increase n here:
n = 2*n;
then you write past the end of your array here:
for (int i=0; i<n; i++)
{
c[i] = 0;
}
which causes undefined behaviour (probably overwrites some other variables)