Need help answering this question; I understand it I think, but I don't know how to explain it

[nimble merlin]

Try looking at the region bounded by y = 0 and y = x(x^2 - 1).
You will see the difference between these definitions.

[gray orchid]

I'm sorry, I thought the second definition wasn't even a proper region. Could you explain to me where I'm missing something? I don't quite understand

[nimble merlin]

The point is that part even though the region is between y = f(x) and y = g(x), that doesn't mean that one of the functions always need to be smaller.
In my example, the region consists of two parts. In one part we have 0 ≤ y ≤ x(x^2 - 1), in another we have x(x^2 - 1) ≤ y ≤ 0.

[gray orchid]

so because of ≤, its possible to have no area?

[nimble merlin]

Not just no area: no region.

[gray orchid]

thanks man!

[wary thunder]

@gray orchid has given 1 rep to @nimble merlin