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

1 Answer
Mar 19, 2018

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.