1 using integration by parts. Example 2 a). Draw the curve 6 y2 = x (x 2)2 – b). Find the point of intersection of the curve with x-axis. b) c). Calculate the length of the loop of the curve y2 = Let 6 y2 = x (x – 2)2 Differentiating with to x 0 1 1 2 6 Figure 3 x (x 2)2 – dy 12 y dx = (x 2)2 + 2 x (x 2) – – = (x 2) (3x 2) – – dy = dx 12 y 2 1  (x 2)2 (3x 2)2 1   24x(x 2)2 (x 2)2 (3x 2)2 = 24x(x 2)2 (3x 2)2 = 1  24x dx a 1  2 Length of the loop = 2 x0 dx 24x = (3x 2)  0 dx 2
1 using integration by parts. Example 2 a). Draw the curve 6 y2 = x (x – 2)2 b). Find the point of intersection of the curve with x-axis. c). Calculate the length of the loop of the curve y2 = 0 1 2 Figure 3 b) Let 6 y2 = x (x – 2)2 Differentiating with to x 1 6 x (x – 2)2 12 y dy dx = (x – 2)2 + 2 x (x – 2) dy dx = (x – 2) (3x – 2) = 12 y 1   1  2 (x 2)2 (3x 2)2 24x(x 2)2 = (x 2)2 (3x 2)2 24x(x 2)2 = 1  (3x 2)2 24x Length of the loop = a 2 x0 1  dx dx 2 = 2 0 (3x  2) 24x dx
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