1-x² 1. The curve C has equation y = B (i) Express 1-x² 1+x² in the form A + where the values of A and B are to be determined. 1+x² (ii) Hence, find the exact value of the area of the region bounded by the curve C and the x-axis. 1+x²1

x2 +7 dx 2 Use residues to find (1+ x²)²

Find the area of the shaded region. f(x) = x3+3x2-9x-12g(x) = 4x+3

Use the five rectangles in Figure, to find two approximations of the area of the region lying between the graph of f(x) = −x2 + 5 and the x-axis between x = 0 and x = 2.