Simpson's Rule (interpolating quadratic polynomials)
> | CurveFitting:-PolynomialInterpolation( [a, a+h, a+2*h], [f(a), f(a+h), f(b)], x ); |
> | int( %, x = a..a+2*h ); |
> | simplify( %, size ); |
Simpson's 3/8 Rule (interpolating cubic polynomials)
> | CurveFitting:-PolynomialInterpolation( [a, a+h, a+2*h, a+3*h], [f(a), f(a+h), f(a+2*h), f(b)], x ); |
> | int( %, x = a..a+3*h ); |
> | simplify( %, size ); |
Boole's Rule (interpolating quartic polynomials)
> | CurveFitting:-PolynomialInterpolation( [a, a+h, a+2*h, a+3*h, a+4*h], [f(a), f(a+h), f(a+2*h), f(a+3*h), f(b)], x ); |
> | int( %, x = a..a+4*h ); |
> | simplify(%, size); |
11-Point Newton-Cotes Rule
> | CurveFitting:-PolynomialInterpolation( [seq( a + i*h, i = 0..10 )], [seq( f(a + i*h), i = 0..9 ), f(b)], x ); |
> | int( %, x = a..a+10*h ); |
> | simplify(%, size); |