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.

$\mathrm{with}\left(\mathrm{student}\right)\:$

$\mathrm{leftbox}\left(x^4\ln \left(x\right)\,x=2..4\,\mathrm{color}=\mathrm{RED}\right)$

$\mathrm{leftbox}\left(\sin \left(x\right)x+\sin \left(x\right)\,x=0..2\mathrm{\pi }\,5\,\mathrm{shading}=\mathrm{BLUE}\right)$

$\mathrm{leftsum}\left(\sin \left(x\right)x+\sin \left(x\right)\,x=0..2\mathrm{\pi }\,5\right)$

$\frac{2\mathrm{\pi }\left(\sum _{i=0}^4\left(\frac{2\sin \left(\frac{2i\mathrm{\pi }}{5}\right)i\mathrm{\pi }}{5}+\sin \left(\frac{2i\mathrm{\pi }}{5}\right)\right)\right)}{5}$

$\mathrm{value}\left(\right)$

$\frac{2\mathrm{\pi }\left(-\frac{6\sin \left(\frac{2\mathrm{\pi }}{5}\right)\mathrm{\pi }}{5}-\frac{2\sin \left(\frac{\mathrm{\pi }}{5}\right)\mathrm{\pi }}{5}\right)}{5}$

$\mathrm{evalf}\left(\right)$

$\mathrm{-5.433738028}$