Mathematics

Problem

A region

P

is bounded on the left by

x = 0

and on the right by the piecewise curve

x = 4 - y

for

-2 \le y \le 0

x = 4 + y

for

0 \le y \le 2

, and

x = 8 - y

for

2 \le y \le 4

. Find the exact area of region

P