∫x^4e^-xdx, x∈[0, ∞] is _______ (a) 12 (b) 4 (c) 4! (d) 64

Question

\(\int\limits_0^∞\) x⁴e^-xdx is _______

(a) 12

(b) 4

(c) 4!

(d) 64

Answer 1

(c) 4!

 \(\int\limits_0^∞\) x⁴e^-xdx = \(\int\limits_0^∞\)xⁿe^-axdx = n!/a^{n + 1}

Here n = 4, a = 1 = 4!/1⁵ = 4!