can someone help me, i already try but im stuck
Notice that Simpson's 3/8 rule can be derived by integrating the third-degree Lagrange interpolating polynomial that fits to four equally spaced points, [math]x_0, x_1, x_2, x_3[/math] Prove
[math]\int_{x_0}^{x_3} \frac{(x-x_1)(x-x_2)(x-x_3)}{(x_0-x_1)(x_0-x_2)(x_0-x_3)} f(x_0)\,dx \approx \frac {3h}{8} f(x_0) ,[/math]
which comes out in the course of deriving Simpsons's 3/8 rule
Notice that Simpson's 3/8 rule can be derived by integrating the third-degree Lagrange interpolating polynomial that fits to four equally spaced points, [math]x_0, x_1, x_2, x_3[/math] Prove
[math]\int_{x_0}^{x_3} \frac{(x-x_1)(x-x_2)(x-x_3)}{(x_0-x_1)(x_0-x_2)(x_0-x_3)} f(x_0)\,dx \approx \frac {3h}{8} f(x_0) ,[/math]
which comes out in the course of deriving Simpsons's 3/8 rule
