integral_inside_loop

        // calculating the integral each timestep
        double integral = 0.0;
        double E_n = 1.5 * T_n;

        // creating histogram each timestep
        for (int i = 0; i < n_e; i++){
            int bin = (int)( (electrons[i].energy - Emin)/bin_width );
            if (bin >=0 && bin < N)
            histo_maxwell[bin]++;
        }

        for (int i = 0; i < N; i++){
            double bin_center = Emin + (i + 0.5) * bin_width;
            integral+= (bin_center - E_n)*elastic_vec[i]*sqrt(bin_center)*( static_cast<double>(histo_maxwell[i])/(electrons.size()*bin_width) ) * delta * (N_He/Volume) * sqrt(2*q/m_e) * bin_width; //
        }

        E_mean -= integral*dt;

        file10 << t*dt << " " << E_mean << "\n";

        for (int i = 0; i < N; i++){
            histo_maxwell[i] = 0;
        }


        // calculating mean energy
        double total_energy = 0.0;
        for (const auto& e : electrons) total_energy += e.energy;
        double mean_energy = total_energy / n_e;
        file8 << t*dt << " " << mean_energy << "\n";