Calculating Area of Polar Curve: Help Needed!

[schaefer]

I've got a test tomorrow and I can't figure this one out:

r^{2} = 9cos(5\vartheta)

I picked the inteval from 0 to \pi/2 and I keep getting 18/5 but the back of the book says the answer is 18. I think something is wrong with my interval. Help Please!

 

[mathslover]

when the angle changed from 0 to pi/2 ,you DON'T get the whole curve!
Try drawing out the curve.Note, cos(5*angle) must be > 0 to give a real point on the curve.

when angle=0, r=3
when angle=18 degree, r=0hope this is helpful