3. Let S be the closed region in the first quadrant of the xy-plane bounded by

,

the y-axis, and the x-axis. What is

A 27/2

B 27

C 162/5

D 324/5

E 81

Solution C

The domain of integration is a quarter circle of radius 3 in the first quadrant. Consequently, switching to polar coordinates, the double integral is equal to