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 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.

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