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Project. Approximating In 2 and π by numerical integration. 1. In Calculus 1 you learned that the natural logarithm of the number 2 is the value of the integral da The value of In 2 correct to 15 decimal places is In2 0.693147180559945 Use the error formula for the Composite Simpson's rule to determine how many correct decimal places you can obtain when you partition [1,2] into 4, n 8, and12 equal-length subintervals. 2. In Calculus you learned how to find the value of the integral -dr = arctan | = arctan 1-arctan 0 =- It follows that the number is the value of the integral The value of π to 15 decimal places is 3.141592653589793 Taking (a)-1t. hand the derivatives f"() and f4) as needed to apply the error estimates of the Simpson's rule and the Trapezoidal rule. Instead, a computer algebra system yields 1 + r2, it would be somewhat lengthy to first calculate and then maximize by !"(x) = 8(3x2-1) and the maximum of both If"(x)l and lf(4)(z)l is attained at = 0 Use the error formula for the Composite Simpson's rule to determine how1 decimal places you can obtain when you partition [0,1]into 4, n 8, an equal-length subintervals. many correct 12

Answer 1

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According to rules and regulations we are able to do only one questipn at a time.. so i do only 1st..

a: max x) 2. У r,y - du a hal2 do a