Unformatted text preview: ) that interpolates the function f ( x ) at the points x , x 1 , x 2 , and x 3 . (c) Integrate the interpolating polynomial P 3 ( x ) to derive the following Newton-Cotes formula often referred to as Simpson’s three-eigths rule : Z x 3 x f ( x ) dx ≈ 3 h 8 h f ( x ) + 3 f ( x 1 ) + 3 f ( x 2 ) + f ( x 3 ) i . 4. Consider the following integral: Z 4 3 x √ x 2-4 dx. Compute this integral: (a) Exactly by hand. (b) Approximately with the Trapezoidal rule and compute the error (error = | approx-exact | ). (c) Approximately with Simpson’s rule and compute the error (error = | approx-exact | ). (d) Approximately with Simpson’s three-eigths rule and compute the error (error = | approx-exact | ). 1...
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This note was uploaded on 12/11/2011 for the course MATH 174 taught by Professor Staff during the Fall '08 term at UCSD.
- Fall '08