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

The function simpson approximates a definite integral using Simpson's rule.  If the parameters are symbolic, then the formula is returned.

Four equal-sized intervals are used by default.

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

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

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

$\frac{3^k\ln \left(3\right)}{6}+\frac{2\left(\sum _{i=1}^2{\left(\frac{1}{2}+i\right)}^k\ln \left(\frac{1}{2}+i\right)\right)}{3}+\frac{\left(\sum _{i=1}^1{\left(1+i\right)}^k\ln \left(1+i\right)\right)}{3}$

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

$\frac{\sin \left(1\right)}{9}+\frac{2\sin \left(3\right)}{9}+\frac{2\left(\sum _{i=1}^6\left(\sin \left(\frac{5}{6}+\frac{i}{3}\right)\left(\frac{5}{6}+\frac{i}{3}\right)+\sin \left(\frac{5}{6}+\frac{i}{3}\right)\right)\right)}{9}+\frac{\left(\sum _{i=1}^5\left(\sin \left(1+\frac{i}{3}\right)\left(1+\frac{i}{3}\right)+\sin \left(1+\frac{i}{3}\right)\right)\right)}{9}$