student(deprecated)/middlesum - Help

student

 middlesum
 numerical approximation to an integral

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

Parameters

 f(x) - algebraic expression in x x - variable of integration a - lower bound for the range of integration b - upper bound for 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][RiemannSum] instead.
 • The function middlesum computes a numerical approximation to a definite integral using rectangles. The height of each rectangle (box) is determined by the value of the function at the midpoint of each interval.
 • Four equal-sized intervals are used by default.
 • The command with(student,middlesum) allows the use of the abbreviated form of this command.

Examples

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

 > $\mathrm{with}\left(\mathrm{student}\right):$
 > $\mathrm{middlesum}\left({x}^{k}\mathrm{ln}\left(x\right),x=1..3\right)$
 $\frac{{1}}{{2}}{}{\sum }_{{i}{=}{0}}^{{3}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}{\left(\frac{{5}}{{4}}{+}\frac{{1}}{{2}}{}{i}\right)}^{{k}}{}{\mathrm{ln}}{}\left(\frac{{5}}{{4}}{+}\frac{{1}}{{2}}{}{i}\right)$ (1)
 > $\mathrm{middlesum}\left(\mathrm{sin}\left(x\right)x+\mathrm{sin}\left(x\right),x=1..3,12\right)$
 $\frac{{1}}{{6}}{}{\sum }_{{i}{=}{0}}^{{11}}\phantom{\rule[-0.0ex]{5.0px}{0.0ex}}\left({\mathrm{sin}}{}\left(\frac{{13}}{{12}}{+}\frac{{1}}{{6}}{}{i}\right){}\left(\frac{{13}}{{12}}{+}\frac{{1}}{{6}}{}{i}\right){+}{\mathrm{sin}}{}\left(\frac{{13}}{{12}}{+}\frac{{1}}{{6}}{}{i}\right)\right)$ (2)