## Thomas' Calculus 13th Edition

$| Error| \lt 0.00064$
Integrate the integral with respect to $x$ as follows: $f(x)=\int_0^{x} t^2 e^{-t^2} \space dt \space \\=\int_0^{x} [t^2-t^4+\dfrac{t^6}{2 !} -\dfrac{t^{8}}{3!}-...] \space dt \\ =\dfrac{x^3}{3}-\dfrac{x^{5}}{5}+\dfrac{x^{7}}{7 \cdot 2!}-\dfrac{x^{9}}{9 \cdot 3!}+\dfrac{x^{11}}{11 \cdot 4!} ....$ Now, the error can be found as follows: $| Error| \lt \dfrac{1}{13\cdot 5 !} \approx 0.00064$ and $| Error| \lt 0.00064$