a) Prove that the improper integral «£° e-x2 dx converges to a finite real number. b) Prove that if f is the value of the

a) Prove that the improper integral ˆ«£° e-x2 dx converges to a finite real number.
b) Prove that if f is the value of the integral in part a), then

c) Show that

d) Let Qk represent the n-dimensional cube [-k, k] × ˆ™ ˆ™ ˆ™ × [-k, k]. Find

2= lim e'r dr de. N-700 Jo