Question

Which one of the improper integrals below converges or diverges?
[int _a ^b] means integral from a to b, we use inf to indicate infinity.

a) [int _0 ^1] 1/x dx
b) [int _0 ^1] 1/x^(1/2) dx
c) [int _0 ^1] 1/x^2 dx

d) [int _1 ^inf] 1/x dx
e) [int _1 ^inf] 1/x^(1/2) dx
f) [int _1 ^inf] 1/x^2 dx

g) [int _1 ^inf] lnx / x^2 dx
h) [int _1 ^inf] lnx / x dx

i) [int _(-inf) ^inf] 1/(1+x^2) dx
j) [int _1 ^inf] exp(-x^2) dx
k) [int _1 ^inf] (sinx / x )^2 dx
l) [int _2 ^inf] 1 / sqrt(x^2 - 1) dx
m) [int _0 ^Pi/2] tanx dx

Answer 1

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