Does the integral converge or diverge

MATHEMATICS · Subjective · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Does the integral ∫0∞x2e−x dx\displaystyle \int_{0}^{\infty} x^{2} e^{-x}\,dx converge or diverge? Provide your conclusion and a brief justification based on the behavior of the integrand near each improper limit.

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