Which of the following is an improper integral?

a) integral from 0 to 3 of (x+1)/(3x-2) dx
b) integral from 0 to 3 of (x+1)/(3x-2) dx
c) integral from 0 to 3 of (x+1)/(3x-2) dx
d) None of these

Why are the first three answers identical?

what happens when x= 2/3 ? Look at the (3x-2) term

I am sorry. These are the options:

a) integral from 0 to 3 of (x+1)/(3x-2) dx
b) integral from 1 to 3 of (x+1)/(3x-2) dx
c) integral from -1 to 0 of (x+1)/(3x-2) dx
d) None of these

please help me

To determine which of the following integrals is improper, we need to check if any of the integrals have infinite limits or if there are discontinuities or singularities in the interval of integration.

Let's analyze each option:

a) The integral is from 0 to 3, which is a finite interval. Therefore, it is not an improper integral.

b) The integral is from 0 to 3, which is a finite interval. Therefore, it is not an improper integral.

c) The integral is from 0 to 3, which is a finite interval. Therefore, it is not an improper integral.

d) Since none of the given options involve infinite limits or have discontinuities or singularities in the interval of integration, the answer is "None of these."

In conclusion, none of the given options represent an improper integral.