simple yet hard finding area + volume question

Calculate the area bounded by the curves

y1= 1/x^1/2 and y2 = x^1/2+1/x from x=2 and x=1

ok... a simple sketch should indicate that the integral is

S 2-1 y2-y1 dx

doing all the necessary steps you should get (if im correct) [ln(x)]2-1

the answer is ln(2) * please check if im correct or not :)

part b) now the limits change.. its x=1 and x= infinity ....

the area is infinity because ln(infinity) = infinity ?? is that strong enough argument ??? * please check once again :)

part c) calculate the volume now of that region about the x axis...

well simple

volume is

pi S 2-1 (y2)^2 - (y1)^2 * is this correct :) just checking xD

and if you do all the correct simplifying and integration you should get

pi(9/2-4/2^1/2) ... ?? * please check again xD

same thing as part b) let the new limits b x=1 and x= infinity... prove that the volume is infinity.. same arugment as part b ??

thanks guys :)