Question

1. Consider the following integral: \int_0^3 e^x \sin(x)dx Write a Python program to evaluate this integral using Simpson's 1/3 rule. Input the lower and upper limits and the first n from the keyboard. Put the 1/3 rule and the integrand in separate functions. Note: you will need to include logic to account for the alternating 4's and 2's. Use two for loops or alternate the factors 4 and 2. In the main program first check your input to see that the input value of n is even. If not, print a warning and leave the program. Begin with n = 4. Compute the relative error, Ea, as the difference between the present result and the previous result. (For n = 4 the previous value is zero.) Put the call to Simpson inside a while loop and double n each time until you get an Ea value less than 10^{-5} in magnitude or you have made 15 attempts. Print to the output file a, and from the main program. Print n, your answer, and Ea for each value of n within the while loop. Compare your value for n = 4 to the hand solution.

          1. Consider the following integral:
\int_0^3 e^x \sin(x)dx
Write a Python program to evaluate this integral using Simpson's 1/3 rule.
Input the lower and upper limits and the first n from the keyboard. Put the 1/3
rule and the integrand in separate functions. Note: you will need to include logic
to account for the alternating 4's and 2's. Use two for loops or alternate the
factors 4 and 2. In the main program first check your input to see that the input
value of n is even. If not, print a warning and leave the program.
Begin with n = 4. Compute the relative error, Ea, as the difference between
the present result and the previous result. (For n = 4 the previous value is zero.)
Put the call to Simpson inside a while loop and double n each time until you get
an Ea value less than 10^{-5} in magnitude or you have made 15 attempts.
Print to the output file a, and from the main program. Print n, your
answer, and Ea for each value of n within the while loop. Compare your value for
n = 4 to the hand solution.

1. Consider the following integral:
∫0^3 e^x sin(x)dx
Write a Python program to evaluate this integral using Simpson's 1/3 rule.
Input the lower and upper limits and the first n from the keyboard. Put the 1/3
rule and the integrand in separate functions. Note: you will need to include logic
to account for the alternating 4's and 2's. Use two for loops or alternate the
factors 4 and 2. In the main program first check your input to see that the input
value of n is even. If not, print a warning and leave the program.
Begin with n = 4. Compute the relative error, Ea, as the difference between
the present result and the previous result. (For n = 4 the previous value is zero.)
Put the call to Simpson inside a while loop and double n each time until you get
an Ea value less than 10^-5 in magnitude or you have made 15 attempts.
Print to the output file a, and from the main program. Print n, your
answer, and Ea for each value of n within the while loop. Compare your value for
n = 4 to the hand solution.

Added by Nathaniel C.

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