Word Count : 220

---

To approximate the integral: \[ I = \int_0^1 \frac{dx}{1+x^2} \] using the Composite Simpson’s Rule with step sizes \( h = 0.25 \) and \( h = 0.125 \), and then refining the result with Romberg Integration, we proceed as follows: ### Step 1: Composite Simpson's Rule The Simpson’s Rule formula for \( n \) ____ __________ ___ _________ _________ _________ ____ ___ __________ ____.
_________ ____ _________ _________ _____ ___.
___ ______ ____ ___ _____ _____ ______ _____ ____ _________ ____ _________.
__________ _________ ___ ______ ______ _________ _________ ____ ___ _____ ___ _______.
__________ ______ _______ ______ ___ _________.
_____ _____ ___ ___ ________ _________ _______ ________.
______ _________ __________ ___ _______ ________ ___ ____ _________ ________ ________ ______.
____ __________ _____ _____ ___ ___ ___ ___.
________ ______ ______ __________ ______ _____ _______ _____ _________ ____ __________.
________ ________ ______ ____ ______ __________ ______ ______ _________.
__________ __________ __________ ____ ________ ________ ______ ____ __________ _______.
_______ __________ _______ ____ ________ ________ ____.
________ _________ _______ ______ _____ _________ ____ _______ ____.
_______ ___ ____ __________ ____ __________ ___ ___ _____ ____.
___ __________ _________ _________ __________ ___ ____ _________ __________ _____ ______.
___ __________ ___ _________ __________ _________ ______.
_______ ______ ______ __________ ____ ___ ______ ________ _________.
_______ _________ _____ _______ _________ _____ _________.
____.
Get Full Answer on WhatsApp