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If this limit exists and is finite, the integral converges. Otherwise, it diverges. For example, let's evaluate ∫[1 to ∞] (1/x³) dx. We rewrite it as lim[t→∞] ∫[1 to t] (1/x³) dx. Evaluating the integral, we get lim[t→∞] [-1/(2x²)] evaluated from 1 to t, which simplifies to lim[t→∞] [-1/(2t²) + 1/2]. As t approaches infinity, -1/(2t²) approaches 0, so the limit is 1/2. Therefore, the integral converges, and its value is 1/2.
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