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.

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

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

$\frac{\left(\sum _{i=0}^3{\left(\frac{5}{4}+\frac{i}{2}\right)}^k\ln \left(\frac{5}{4}+\frac{i}{2}\right)\right)}{2}$

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

$\frac{\left(\sum _{i=0}^{11}\left(\sin \left(\frac{13}{12}+\frac{i}{6}\right)\left(\frac{13}{12}+\frac{i}{6}\right)+\sin \left(\frac{13}{12}+\frac{i}{6}\right)\right)\right)}{6}$