If $\int_0^k (2x + 1)\,dx = 12$ and $k > 0$, what is $k$?

Explanation

1. 01

   $\int_0^k (2x + 1)\,dx = k^2 + k$.

2. 02

   $k^2 + k - 12 = 0$, so $(k + 4)(k - 3) = 0$; with $k > 0$, $k = 3$.