Recall that 0tdx1x2 tan1t so that in particular 0t4dx1x2

Recall that _0^tdx/(1+x^2) = tan^(-1)t , so that in particular _0^t4dx/(1+x^2) = tan^(-1)1 = Using the error estimates fot the Trapezoidal rule and Simpson\'s rule, calculate how large n should be to calculate correct to d decimal places from this formula using Trapezoidial and Simpson’s, Set format long in MATLAB and get the value of to fifteen decimal places by simply typing pi. Then use your Trapezoidal and Simpson’s functions from parts and to see how large you actually have to choose n to calculate to 5, 10, and 15 decimal places.

Solution

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