I'm getting 11.48 as the answer, assuming that r=3 is a horizontal line.
Graph the two functions on your calculator: y=10sin(x) and y=3.
You'll notice that they are asking for the area between these two curves. I'll be taking vertical strips, so the limits of integration are decided by the x coordinates of the intersection of the two curves. The two x coordinates are: .30469265 and 2.8369.
I now integrate (10sin(x) - 3) from .30469265 to 2.8369 and get 11.48.