G find all the values of p for which the following functions are improperly integrable on the indicated domain. be sure to prove your claims, ie show that it is improperly integrable for those numbers p, but is not for other numbers 1.f(x)=1/x^p on i =(0,1) 2. f(x) = 1/(x(lnx)^p) on I = (e, inf)

1. In order to make the integral improper    must be 1.

2. In order to make the integral improper    must be 1.  

Step-by-step explanation:

Using the rules of integration we get that for

Therefore in order to make that integral improper    must be 1.

If  p = 1     then you would have a 1/0  indeterminate form.

2.   Using the of integration, specifically substitution we get that for

For    we would have

And the problem is the same.  If     we would have a 1/0 indeterminate form.