Sketch the region of integration switch to polar coordinates

Sketch the region of integration, switch to polar coordinates and evaluate the integral:

Because the graph extends entirely about the origin and the origin is contained in the domain, the integral is

201cos0rdrd0201cosrdrd

20(1cos)22d02(1cos)22d

122012cos+cos2d120212cos+cos2d

Using the half angle formula:

122012cos+1+cos(2)2d120212cos+1+cos(2)2d

12[322sin+sin(2)4]2012[322sin+sin(2)4]02

12(30+0)12(30+0)

3232

Paul will need to buy 3232 square meters of flowers.