Question

A region is bounded in the second quadrant by the curve y = ln(1–x), the line y=3, and the y-axis. Find the area of the region.

Answer 1

If you draw this you see you want the integral from y =0 to y = 3 of -x dy

y = ln(1-x)
e^y = 1-x
-x = e^y -1

so integral from 0 to 3
e^y dy - dy

e^y - y at 3 = e^3-3
e^y - y at 0 = 1
so
e^3 - 4

about 20 - 4 = 16

Answer 2

Wolfram amazes me more every day.

http://www.wolframalpha.com/input/?i=area+between+y%3D+ln%281-x%29+%2C+y%3D3+%2C+x%3D0

notice that Damon took horiontal slices, while Wolfram took vertical slices.
Same result of course.