4-21. Do you agree or disagree with statements (a)–(f)? Given that the indicated limits exist:

(a) 4

+∞

a f (x)dx = limb→+∞ 4 b a f (x)dx

(b) 4 b

−a f (x)dx = lima→+∞ 4 b

−a f (x)dx

(c) 4

+∞

−∞ f (x)dx = lima→+∞ 4 a

−a f (x)dx

(d) 4

+∞

−∞ f (x)dx = 4 0

−∞ f (x)dx + 4

+∞

0 f (x)dx (provided that the integrals on the right-hand side of this equation exist).

Moreover, if f (x) is unbounded on [a, b] but bounded on [a+ε, b], ε > 0 and small, then, provided that the indicated limit exists,

(e) 4 b a f (x)dx = lim ε→0

ε>0 4 b a+ε f (x)dx If f (x) is unbounded on [a, b] though bounded on [a, b − ε],ε > 0 and small, then, provided that the indicated limit exists,

(f) 4 b a f (x)dx; = lim ε→0

ε>0 4 b−ε

a f (x)dx In addition, find:

(g) 4 2 0 x−1/2dx

(h) 4

+∞

0 e−1/2xdx

(i) 4

+∞

−∞ e−|x|dx