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

The function leftsum 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 left side of each interval.

Four equal-sized intervals are used by default.

A graph of the approximation can be obtained by the Maple procedure leftbox.

The command with(student,leftsum) allows the use of the abbreviated form of this command.

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

$\mathrm{leftsum}\left(x^k\ln \left(x\right)\,x=1..3\right)$

$\frac{\left(\sum _{i=0}^3{\left(1+\frac{i}{2}\right)}^k\ln \left(1+\frac{i}{2}\right)\right)}{2}$

$\mathrm{leftsum}\left(\sin \left(x\right)x+\sin \left(x\right)\,x=1..3\,12\right)$

$\frac{\left(\sum _{i=0}^{11}\left(\sin \left(1+\frac{i}{6}\right)\left(1+\frac{i}{6}\right)+\sin \left(1+\frac{i}{6}\right)\right)\right)}{6}$