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Comparison between trapezoidal rule and Simpsons rule
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written 5.7 years ago by
teamques10
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• modified 5.6 years ago |
| Sr.no | Trapezoidal rule | simpson's rule |
|---|---|---|
| 1 | Area of irregular piece of land obtain by trapezoidal rule is not accurate like Simpson’s rule | Area of irregular piece of land obtain by Simpson’s rule the |
| 2 | In this method the boundary between the end of ordinate and straight line. Thus the area enclosed between the baseline and the irregular boundary is dividing into series of trapezoids. | In this method required baseline even number of division of the area i.e. the total number of ordinate must be odd. If there is a then the the of an last division must be determine separately. |
| 3 | $ A = {\frac{h}{2}}[{({y_1 + y_2})+({y_2 + y_3})+....+({y_n + y_{n+1})}}]\\ [{({y_1 + y_2})+({y_2 + y_3})+....+({y_n + y_{n+1})}}]$ = sum of all parallel ordinate or offset ; n=1,2,3,4 ; h = width of strip | $ A = {\frac{h}{3}}[{({y_1 + y_n})+4({y_2 + y_4 + ...}) + 2({y_3 + y_5 + ...})}] \\ ({y_1 + y_n})$ =sum of extreme ordinate ; $({y_2 + y_4 + ...})$ =sum of even ordinate ; $ ({y_3 + y_5 + ...})$ =sum of odd ordinate ; h=width of strip |
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