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 NewtonCotes formula often referred to as Simpson’s threeeigths 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 24 dx. Compute this integral: (a) Exactly by hand. (b) Approximately with the Trapezoidal rule and compute the error (error =  approxexact  ). (c) Approximately with Simpson’s rule and compute the error (error =  approxexact  ). (d) Approximately with Simpson’s threeeigths rule and compute the error (error =  approxexact  ). 1...
View
Full Document
 Fall '08
 staff
 Math, Numerical Analysis, Polynomial interpolation, cubic spline

Click to edit the document details