Understanding Gaussian Integral: Question on Hinch's Perturbation Theory Book

[liyz06]

Homework Statement

I'm reading Hinch's perturbation theory book, and there's a statement in the derivation:
...$\int_z^{\infty}\dfrac{d e^{-t^2}}{t^9}<\dfrac{1}{z^9}\int_z^{\infty}d e^{-t^2}$...

Why is that true?

Homework Equations

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Dick]

Homework Statement

I'm reading Hinch's perturbation theory book, and there's a statement in the derivation:
...$\int_z^{\infty}\dfrac{d e^{-t^2}}{t^9}<\dfrac{1}{z^9}\int_z^{\infty}d e^{-t^2}$...

Why is that true?

Homework Equations

The Attempt at a Solution

Because 1/t^9 for t in (z,infinity) is less than 1/z^9. Draw a graph.

 

[liyz06]

Because 1/t^9 for t in (z,infinity) is less than 1/z^9. Draw a graph.

Thanks, really stupid question