Use the Error Bound to find the least possible value of N for which $Error(S_N) \le 1\times 10^{-9}$ in approximating

$\int^{1}_{0}{3e^{x^{2}}} \, dx$

using the result that $$Error(S_{N}) \le \frac{K_4(b - a)^5}{180N^4},$$ where $K_4$ is the least upper bound for all absolute values of the fourth derivatives of the function $3e^{x^{2}}$ on the interval $[a,b]$.

$N =$

Hint: