1. Given the curve y = x2 – 4, calculate, correct to two decimal places, the :

   1. area of the finite region bounded by the curve and the x-axis;
   2. volume generated by rotating the region in (a) through 360o about the x-axis.

   [Take π =  ].

The report stated that this question was attempted by majority of the candidates and they performed well in it. They were able to obtain the points where the curve intersects the x-axis as (-2, 0) and (2, 0). Using the x-coordinate of the point of intersection as the limits of integration, the area was obtained as Area =  =10 or 10.67 sq. units. The volume generated was calculated as  volume = π = 107.28 cubic units.