Numerical methods questions | form six Pure Advanced Mathematics

Find Numerical methods examination questions, form six Pure Advanced Mathematics in acaproso.com

#	Question
1	The value $A=int_{a}^{b}f(x)dx$ represents the area under the graph of $y=f(x)$ between x=a and x=b. Derive the Trapizium rule with 6 ordinates to find an approximation of $A=int_{a}^{b}f(x)dx.$ Using the trapezium rule obtained in (a), approximate $A=int_{1}^{7}frac{x^{3}}{1+x^{4}}dx.$ correct to three decimal places. Evaluate the actual integgral of $A=int_{1}^{7}frac{x^{3}}{1+x^{4}}dx.$ and then calculate the relative error in the approximation obtained in (b). (Give your answers correct to three decimal places). Mathematical Calculation
2	Approximate the value of $int_{3}^{7}frac{1}{x-2}dx$ correct to four decimal places by using The trapezoidal rule with five ordinates and The simpson`s rule with five ordinates. Evaluate the exact value of the integral $int_{3}^{7}frac{1}{x-2}dx$ and compare your answer with those found in part(a) above. Mathematical Calculation

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