Example 4 6 Find , given the following values, using ydx 0 i) Simpsons Rule for the interval (0 6) x≤ ≤ ii) Trapezoidal Rule for the interval (0 x ≤ ≤6) X 0 1 2 3 4 5 6 Y 8 12 14 11 9 3 1 Solution i) Area under curve using Simpsons Rule Y0 = 8 Y0 = 8 125 Y1 = 12 4Y1 = 48 Y2 = 14 2Y2 = 28 Y3 = 11 4Y3 = 44 Y4 = 9 2Y4 = 18 Y5 = 3 4Y5 = 12 Y6 = 1 Y6 = 1 Total Sum 159 6 0 h = 6 =1 Approximate area in therefore. A = 1 h(y0 + 4y1 + 2y2 + 4y3 + 2y4 + 4y5 + y6) 3 = 1 (1)(159) 3 = 53 sq ii) Area under curve using Trapezoidal Rule (≤ 6) Y0 = 8 Y0 = 8
Example 4 Find 6 0 ydx , given the following values, using i) Simpsons Rule for the interval (0 ≤ x≤ 6) ii) Trapezoidal Rule for the interval (0 ≤ x ≤6) X 0 1 2 3 4 5 6 Y 8 12 14 11 9 3 1 Solution i) Area under curve using Simpsons Rule Y0 = 8 Y0 = 8 125 Y1 = 12 4Y1 = 48 Y2 = 14 2Y2 = 28 Y3 = 11 4Y3 = 44 Y4 = 9 2Y4 = 18 Y5 = 3 4Y5 = 12 Y6 = 1 Y6 = 1 Total Sum 159 h = 6 0 6 =1 Approximate area in therefore. A = 1 h(y0 + 4y1 + 2y2 + 4y3 + 2y4 + 4y5 + y6) 3 = 1 (1)(159) 3 = 53 sq ii) Area under curve using Trapezoidal Rule (≤ 6) Y0 = 8 Y0 = 8
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