I will copy down the whole problem.

Part of the design of a stained glass window is shown. The two loops enclose an area of blue glass. The remaining area within the rectangle ABCD is red glass.

*Imagine the rectangle ABCD is tangential....
*another small thing, this graph is supposed to have a shaded region. I dont know which region is shaded. Sorry.

The loops are described by the curve with the parametric equations:

x = 3 cos t ; y = 9 sin 2t ; 0 =< t < 2(pie)

a. Find the cartesian equation of the curve in the form y^2 = f(x). [could do this]
b. Show that the shaded area enclosed bu the curve and the x-axis, is given by

           /  (pie)/2
           |           A sin (2t) sint dt
           /   0
*here is my problem

I find that A = -27, but the books says that its +27. Common sense tells me A cannot be -27, cause that way the area will be negative. That aside, mathematically its negative according to me. Where did i go wrong?