if, f(x) = x^2e^-2x, x ≥ 0, f(x) = 0, otherwise, then evaluate ∫f(x)dx, x∈[0, ∞]

Question

If, \( f(x) = \begin{cases} x^2e^{-2x},x≥0 \\ 0, otherwise\end{cases} \), then evaluate \(\int\limits_{0}^{∞}\)f(x)dx

Answer 1

\(\int\limits_{0}^{∞}\)x²e^-2xdx