geometric applications of the definite integral

1. Find the area under the curve y = x3 - 3x2 - x + 3 from x = 0 to x = 2. 2. Find the area bounded by the curves xy = 1, y = x, x = 2 and y = 0. 3. Find the area bounded by the curves y = x2 - 2x and y = x. 4. Find the area bounded by the curves x2 = 4y and y = 8 x2+4 5. Find the area enclosed by the rose r = 4 cos 20. 6. Find the area common to the circle r = 5 cos 0 and the limacon r = 2 + cos 0