Can you find the area of the region?

Question

y = x-2 /x

Answer 1

y = (x-2)/x = 1 - 2*x^(-1)

the integral is x - 2*ln|x|

x=4: 4 - 2*ln|4| = 4 - 2*ln|2*2| = 4 - 2*( ln|2|+ln|2) = 4 - 2*2ln|2| = 4 - 4*ln|2|

x=2: 2 - 2*ln|2|

4-4*ln|2| - 2+ 2*ln|2| = 2 - 2*ln|2| which is approximately 0.61705+

As a sanity check, the region is ABOUT the same as the right triangle with

base 4-2=2 and height 0.5. THe area is then (1/2)(2)*0.5 = 0.5