Question

Which of the following are improper integrals?

Which of the following are improper integrals? Check all that apply.

a) `int_1^∞` `sin(x)/x` dx

b) `int_4^5` `1/x` dx

c) `int_3^4` `1/sin(x)` dx

d) `int_-3^3` `x^(-1/3)` dx

Answer 1

a, c, d

Explanation:

a) is improper because one of the limits of integration is infinite.

b) because `sin(pi) = 0`, so the integrand is undefined at `pi` which is in the interval of integration.

d) because the integrand is undefined at `0` and `0` is in the interval over which we are integrating.