SOLVED:A possible rule for obtaining an approximation to an integral is the mid-point rule, given by ∫x0^x0 Δx f(x) d x=Δx f(x0 (1)/(2) Δx) O(Δx^3) Writing h for Δx, and evaluating all derivates at the mid-point of the interval (x, x Δx), use a Taylor series expansion to find, up to O(h^5), the coefficients of the higher-order errors in both the trapezium and mid-point rules. Hence find a linear combination of these two rules that gives O(h^5) accuracy for each step Δx.
SOLVED:A possible rule for obtaining an approximation to an i…
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