Mathematics

This integral tests whether you recognize a rational function with a removable discontinuity—and more importantly, whether you check the domain first. The denominator $x^2 - 4 = (x-2)(x+2)$ has a zero at $x = 2$, which lies inside your integration interval $[0,4]$. Before applying any antiderivative formula, you need to decide: does this integral converge, or does it diverge at that singularity? That decision determines everything that follows.

This integral tests whether you recognize a rational function with a removable discontinuity—and more importantly, whether you check the domain first. The denominator $x^2 - 4 = (x-2)(x+2)$ has a zero at $x = 2$, which lies inside your integration interval $[0,4]$. Before applying any antiderivative formula, you need to decide: does this integral converge, or does it diverge at that singularity? That decision determines everything that follows.