student(deprecated)/simpson - 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.

 > $\mathrm{with}\left(\mathrm{student}\right):$
 > $\mathrm{simpson}\left({x}^{k}\mathrm{ln}\left(x\right),x=1..3\right)$
 $\frac{{1}}{{6}}{}{{3}}^{{k}}{}{\mathrm{ln}}{}\left({3}\right){+}\frac{{2}}{{3}}{}{\sum }_{{i}{=}{1}}^{{2}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}{\left(\frac{{1}}{{2}}{+}{i}\right)}^{{k}}{}{\mathrm{ln}}{}\left(\frac{{1}}{{2}}{+}{i}\right){+}\frac{{1}}{{3}}{}{\sum }_{{i}{=}{1}}^{{1}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}{\left({1}{+}{i}\right)}^{{k}}{}{\mathrm{ln}}{}\left({1}{+}{i}\right)$ (1)
 > $\mathrm{simpson}\left(\mathrm{sin}\left(x\right)x+\mathrm{sin}\left(x\right),x=1..3,12\right)$
 $\frac{{1}}{{9}}{}{\mathrm{sin}}{}\left({1}\right){+}\frac{{2}}{{9}}{}{\mathrm{sin}}{}\left({3}\right){+}\frac{{2}}{{9}}{}{\sum }_{{i}{=}{1}}^{{6}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\left({\mathrm{sin}}{}\left(\frac{{5}}{{6}}{+}\frac{{1}}{{3}}{}{i}\right){}\left(\frac{{5}}{{6}}{+}\frac{{1}}{{3}}{}{i}\right){+}{\mathrm{sin}}{}\left(\frac{{5}}{{6}}{+}\frac{{1}}{{3}}{}{i}\right)\right){+}\frac{{1}}{{9}}{}{\sum }_{{i}{=}{1}}^{{5}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\left({\mathrm{sin}}{}\left({1}{+}\frac{{1}}{{3}}{}{i}\right){}\left({1}{+}\frac{{1}}{{3}}{}{i}\right){+}{\mathrm{sin}}{}\left({1}{+}\frac{{1}}{{3}}{}{i}\right)\right)$ (2)