10. Sketch the region bounded by the curves x = | y|, x = 2. Represent the area of the region by one or more integrals (a) in terms of x; (b) in terms of y.

12. Sketch the region bounded by the curves y = x3, y = x2 + x – 1. Represent the area of the region by one or more integrals (a) in terms of x; (b) in terms of y.

18. Sketch the region bounded by the curves x + y = 2y2, y = x3 and find its area.

30. Sketch the region bounded by the three curves y = x3, y = –x, y = 1, and find its area.

34. The region between y = cosx and the x-axis for x in [0,pi/2] is divided into two subregions of equal area by the line x = c. Find c.

36. Set up a definite integral (or integrals) whose value is the area of the region in the first quadrant bounded by the y-axis, the line y = 31/2x, and the circle x2 + y2 = 4.

40. (a) Calculate the area of the region in the first quadrant bounded by the coordinate axes and the graph of the parabola y = 1 + a – ax2, a > 0. (b) Determine a so that the area found in part (a) is a minimum.