Find the area by the given curves

Question

Using the given region enclosed by the given curves find the area.

y=2/x, y=8x, y=x/8, and x>0

Answer 1

integrate from 0 to (1/2) using x/8 and 8x, then from (1.2) to 4 using 2/x and x/8

int(8x-x/8) 0-1/2 = 4x^2-x^2/16 = 1-1/64=63/64

int(2/x-x/8) 1/2-4 = 2ln(x) - x/16 = 2ln4 - 1/4 - (2ln(1/2)-1/32)