How to find a bound for these (simple) integrals With help of $\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$ and $\int_{0}^{\infty} e^{-x} dx =1$, I would like to know how to derive the following bounds:
$$\int_{0}^m 4e^{-\frac{t^2}{8m}}dt \leq 2\sqrt{8\pi m}$$
and
$$\int_{m}^{\infty} 4 e^{-\frac{t}{8}}dt \leq 32.$$
How does one derive these?
So somehow one would do this with change of variables? As I am not very good at such stuff, I would really appreciate any help. 
Thank you very much.

Hint
For the first, change variable $$\frac{t^2}{8m}=x^2$$ so $t=x \sqrt{8m}$, $dt=\sqrt{8m} dx$. So $$I=\int 4e^{-\frac{t^2}{8m}}dt=8 \sqrt{2m}  \int e^{-x^2} dx$$
Do something similar for the second integral.
I am sure that you can take from here.
