Improper Integrals and Area/volume applications

Question

1) f(x)=1/(x-2). The region R is the area between f (x) and the x-axis on the x-interval [3, ∞).

a) Set up an improper integral that can be used to find the area of R.

b) Evaluate the integral from (a). Is the area finite or infinite?

c) Set up an improper integral that can be used to find the volume of the solid created

when R is rotated about the x-axis.

d) Evaluate the integral from (c). Is the volume infinite or finite?

e) **Bonus-type problem** Set up and evaluate an integral to find the volume of the solid

created when R is revolved about the line y = -4.

f) **Bonus-type problem** Set up and evaluate an integral to find the volume of the solid

created when R is revolved about the line y = 5.

Answer 1

f(x)=1/(x-2)

F(x)= ln|x-2|+c

evaluated from 3 to infinity

= ln|infinity-2|- ln|3-2|

= infinity-0

= infinity