Find the area of the domain D which is in the first quadrant and bounded by xy=1, xy=3, y=x, y=3x.

You must paramaterize. It is easiest if you draw a picture.

[(1/3)^(1/2), 1 ] int (3x - 1/x)dx + [1, (3)^(1/2)] int (3/x - x)dx

(3/2 x^2 - ln x) [(1/3)^(1/2), 1 ] + (3 ln x - (x^2/2) [1, (3)^(1/2)]

Performing the arithmetic gives ln 3

A = ln 3