improper integrals

[katyt]

Can someone please help me with this problems.

22. Decide if the integral diverges or converges:
(the integral from 1 to infinity) (2+cosx)/x^2 dx

28. Is the area between y=1/x and y=1/x^2 on the interval from x=1 to x=infinity finite or infinite? Explain.

29. For what values of p does the integral converge or diverge?:
(the integral from 2 to infinity) dx/x(ln(x))^p

thanks
katy

 

[pka]

What have you done?
This is not a homework service

 

[katyt]

i understand this isnt a homework service. i'm not asking anyone to do the problem for me. i dont know where to start, so im just asking for help. i'm assuming i have to do a limit comparison test, but i dont know what to use or what to do

 

[Matt]

Hello katyt,

22. Decide if the integral diverges or converges:
(the integral from 1 to infinity) (2+cosx)/x^2 dx

Do you believe that:

?

28. Is the area between y=1/x and y=1/x^2 on the interval from x=1 to x=infinity finite or infinite? Explain.

What you have to do is compute:

If the integral is infinite, then the area between the two curves is infinite. On the other hand, if you get a finite number for the integral, then the area between the two curves is finite.

29. For what values of p does the integral converge or diverge?:
(the integral from 2 to infinity) dx/x(ln(x))^p

Try the integral test.

 

[katyt]

thanks, i think i can handle it from there.

Katy