Problem 1. (25 points): Determine the value of n required to approximate S 2 1 x+1...

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Problem 1. (25 points): Determine the value of n required to approximate S 2 1 x+1 dx to within 104, and use the value of n obtained to compute the approximation, using the python implementation of Trapezoidal rule, Simpson's 1/3 rule, Simpsons 3/8 rule. Next, compute the integral by hand. Finally report the error in these methods. Can anyone calculate using Simpson's 3/8 rule by hand and on paper? Im having trouble finding my n value for the subintervals. Thank you! Problem 1. (25 points): Determine the value of n required to approximate S 2 1 x+1 dx to within 104, and use the value of n obtained to compute the approximation, using the python implementation of Trapezoidal rule, Simpson's 1/3 rule, Simpsons 3/8 rule. Next, compute the integral by hand. Finally report the error in these methods. Can anyone calculate using Simpson's 3/8 rule by hand and on paper? Im having trouble finding my n value for the subintervals. Thank you!