student(deprecated)/leftbox - Maple Help

student

 leftbox
 graph an approximation of an integral

 Calling Sequence leftbox(f(x), x=a..b, ) leftbox(f(x), x=a..b, n, 'shading'=, )

Parameters

 f(x) - algebraic expression in x x - variable of integration a - left bound of integration b - right bound of integration n - (optional) indicates the number of rectangles to use color - indicates the color used to shade the rectangles plot options - (optional) additional plot options, see ?plot,options

Description

 • Important: The student package has been deprecated. Use the superseding command Student[Calculus1[[RiemannSum] instead.
 • The function leftbox will generate a plot of rectangular boxes used to approximate a definite integral.  The height of each rectangle (box) is determined by the value of the function at the left side of each interval.
 • Four intervals are used by default.
 • The formula for the corresponding numerical approximation to this integral is generated by the Maple procedure leftsum.  It can be computed by using the procedure value or evalf.
 • The command with(student,leftbox) 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.

 > $\mathrm{with}\left(\mathrm{student}\right):$
 > $\mathrm{leftbox}\left({x}^{4}\mathrm{ln}\left(x\right),x=2..4,\mathrm{color}=\mathrm{RED}\right)$
 > $\mathrm{leftbox}\left(\mathrm{sin}\left(x\right)x+\mathrm{sin}\left(x\right),x=0..2\mathrm{\pi },5,\mathrm{shading}=\mathrm{BLUE}\right)$
 > $\mathrm{leftsum}\left(\mathrm{sin}\left(x\right)x+\mathrm{sin}\left(x\right),x=0..2\mathrm{\pi },5\right)$
 $\frac{{2}{}{\mathrm{\pi }}{}\left({\sum }_{{i}{=}{0}}^{{4}}{}\left(\frac{{2}{}{\mathrm{sin}}{}\left(\frac{{2}{}{i}{}{\mathrm{\pi }}}{{5}}\right){}{i}{}{\mathrm{\pi }}}{{5}}{+}{\mathrm{sin}}{}\left(\frac{{2}{}{i}{}{\mathrm{\pi }}}{{5}}\right)\right)\right)}{{5}}$ (1)
 > $\mathrm{value}\left(\right)$
 $\frac{{2}{}{\mathrm{\pi }}{}\left({-}\frac{{6}{}{\mathrm{sin}}{}\left(\frac{{2}{}{\mathrm{\pi }}}{{5}}\right){}{\mathrm{\pi }}}{{5}}{-}\frac{{2}{}{\mathrm{sin}}{}\left(\frac{{\mathrm{\pi }}}{{5}}\right){}{\mathrm{\pi }}}{{5}}\right)}{{5}}$ (2)
 > $\mathrm{evalf}\left(\right)$
 ${-5.433738028}$ (3)