student(deprecated)/simpson - Maple Help

student

 simpson
 numerical approximation to an integral

 Calling Sequence simpson(f(x), x=a..b) simpson(f(x), x=a..b, n)

Parameters

 f(x) - algebraic expression in x x - variable of integration a - lower bound on the range of integration b - upper bound on the range of integration n - (optional) indicates the number of rectangles to use

Description

 • Important: The student package has been deprecated. Use the superseding command Student[Calculus1][ApproximateInt] instead.
 • The function simpson approximates a definite integral using Simpson's rule.  If the parameters are symbolic, then the formula is returned.
 • Four equal-sized intervals are used by default.
 • The command with(student,simpson) allows the use of the abbreviated form of this command.

Examples

Important: The student package has been deprecated. Use the superseding command Student[Calculus1][ApproximateInt] instead.

 > $\mathrm{with}\left(\mathrm{student}\right):$
 > $\mathrm{simpson}\left({x}^{k}\mathrm{ln}\left(x\right),x=1..3\right)$
 $\frac{{{3}}^{{k}}{}{\mathrm{ln}}{}\left({3}\right)}{{6}}{+}\frac{{2}{}\left({\sum }_{{i}{=}{1}}^{{2}}{}{\left(\frac{{1}}{{2}}{+}{i}\right)}^{{k}}{}{\mathrm{ln}}{}\left(\frac{{1}}{{2}}{+}{i}\right)\right)}{{3}}{+}\frac{\left({\sum }_{{i}{=}{1}}^{{1}}{}{\left({1}{+}{i}\right)}^{{k}}{}{\mathrm{ln}}{}\left({1}{+}{i}\right)\right)}{{3}}$ (1)
 > $\mathrm{simpson}\left(\mathrm{sin}\left(x\right)x+\mathrm{sin}\left(x\right),x=1..3,12\right)$
 $\frac{{\mathrm{sin}}{}\left({1}\right)}{{9}}{+}\frac{{2}{}{\mathrm{sin}}{}\left({3}\right)}{{9}}{+}\frac{{2}{}\left({\sum }_{{i}{=}{1}}^{{6}}{}\left({\mathrm{sin}}{}\left(\frac{{5}}{{6}}{+}\frac{{i}}{{3}}\right){}\left(\frac{{5}}{{6}}{+}\frac{{i}}{{3}}\right){+}{\mathrm{sin}}{}\left(\frac{{5}}{{6}}{+}\frac{{i}}{{3}}\right)\right)\right)}{{9}}{+}\frac{\left({\sum }_{{i}{=}{1}}^{{5}}{}\left({\mathrm{sin}}{}\left({1}{+}\frac{{i}}{{3}}\right){}\left({1}{+}\frac{{i}}{{3}}\right){+}{\mathrm{sin}}{}\left({1}{+}\frac{{i}}{{3}}\right)\right)\right)}{{9}}$ (2)