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

The function trapezoid computes a numerical approximation to an integral using the Trapezoidal rule. If symbolic arguments are given, an appropriate formula is generated.

Four equal-sized intervals are used by default.

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

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

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

$\frac{\left(\sum _{i=1}^3{\left(1+\frac{i}{2}\right)}^k\ln \left(1+\frac{i}{2}\right)\right)}{2}+\frac{3^k\ln \left(3\right)}{4}$

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

$\frac{\sin \left(1\right)}{6}+\frac{\left(\sum _{i=1}^{11}\left(\sin \left(1+\frac{i}{6}\right)\left(1+\frac{i}{6}\right)+\sin \left(1+\frac{i}{6}\right)\right)\right)}{6}+\frac{\sin \left(3\right)}{3}$