75 x4 3 x1 128 2 3 3 =42 sq units Example 3 1. Sketch the curve 3x2 2x from x = 0 to x = 3.   y x3 2. Find the area included between the curve y = x3 - 3x2 + 2x and the axis of x from x = 0 to x = 2. 2 3. Evaluate . Interpret your result. 3x2 2x  dx 3 0 Solution a) The following table shows some points on the curve. X 0 1 2 0.5 1.5 2 Y 0 0 0 0.375 -0.375 0 The graph is shown in the figure 0 1 2 Figure 7 b) Part of the area is positive and the other part is negative. Hence we should find each area separately. Area from x =0 to x = 1 is given by 3 3x2 2xdx   A x0 1 76 x4 4
75 x4 3 x1 128 2 3 3 =42 sq units Example 3 1. Sketch the curve y  x3 3x2  2x from x = 0 to x = 3. 2. Find the area included between the curve y = x3 - 3x2 + 2x and the axis of x from x = 0 to x = 2. 3. Evaluate 2 0 3 3x2  2x dx . Interpret your result. Solution a) The following table shows some points on the curve. X 0 1 2 0.5 1.5 2 Y 0 0 0 0.375 -0.375 0 The graph is shown in the figure 0 1 2 Figure 7 b) Part of the area is positive and the other part is negative. Hence we should find each area separately. Area from x =0 to x = 1 is given by A  1 x0 3 3x2  2xdx 76 x4 4
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