It's been way too long, and I'm having trouble integrating a function (with a practical application) that should be easy to do with high school calculus. It seems very simple compared to the questions I see here. But I would like some help integrating it.
Here's what I've got, for constants $T$ and $n$
$$\int n (T - x) ^{n - 1} - {1} dx$$
Here's where I landed:
$${n (T - x) ^ n \over -n} - x + C$$
$$-(T - x)^{n} - x + C$$
But for $T=6$ and $n=2$ and $x=0, \ldots, 5$, I expect to get $11, 20, 27, 32, 35, 36$.