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

This two-dimensional version of the procedure constructs a ``line integral'' of f(x,y) expressed respect to y. In general, the first variables are regarded as parameters of the last.

Lineint uses an ``unevaluated'' form of Maple's int function, and only minor simplifications are performed.

A range can be specified for the parameter, as in (z = a..b).

Use value to force Lineint to evaluate like int.

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

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

$\mathrm{Lineint}\left(f\left(x\,y\right)\,x\,y\right)$

$\int f\left(x\left(y\right)\,y\right)\sqrt{{\left(\frac{\ⅆ}{\ⅆy}x\left(y\right)\right)}^2}\ⅆy$

$\mathrm{Lineint}\left(f\left(x\,y\right)\,x\,y=2..4\right)$

${\int }_2^{4}f\left(x\left(y\right)\,y\right)\sqrt{{\left(\frac{\ⅆ}{\ⅆy}x\left(y\right)\right)}^2}\ⅆy$

$\mathrm{Lineint}\left(f\left(x\,y\right)\,x=t\,y=t^2\right)$

$\int f\left(t\,t^2\right)\sqrt{{\left(\frac{\ⅆt}{\ⅆt}\right)}^2+{\left(\frac{\ⅆ}{\ⅆt}\left(t^2\right)\right)}^2}\ⅆt$

$\mathrm{Lineint}\left(f\left(x\,y\right)\,x\,y\,t=a..b\right)$

${\int }_a^{b}f\left(x\left(t\right)\,y\left(t\right)\right)\sqrt{{\left(\frac{\ⅆ}{\ⅆt}x\left(t\right)\right)}^2+{\left(\frac{\ⅆ}{\ⅆt}y\left(t\right)\right)}^2}\ⅆt$