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 Lineint
 inert Form of Line Integral

 Calling Sequence Lineint(f(x,y), x, y) Lineint(f(x,y), x=x(t), y=y(t)) Lineint(f(x,y), x, y =a..b) Lineint(f(x,y,z), x, y, z)

Parameters

 f(x, y) - expression in x and y a, b - (optional) lower and upper bounds

Description

 • 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.

Examples

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

 > $\mathrm{with}\left(\mathrm{student}\right):$
 > $\mathrm{Lineint}\left(f\left(x,y\right),x,y\right)$
 ${∫}{f}{}\left({x}{}\left({y}\right){,}{y}\right){}\sqrt{{\left(\frac{{ⅆ}}{{ⅆ}{y}}{}{x}{}\left({y}\right)\right)}^{{2}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{y}$ (1)
 > $\mathrm{Lineint}\left(f\left(x,y\right),x,y=2..4\right)$
 ${{∫}}_{{2}}^{{4}}{f}{}\left({x}{}\left({y}\right){,}{y}\right){}\sqrt{{\left(\frac{{ⅆ}}{{ⅆ}{y}}{}{x}{}\left({y}\right)\right)}^{{2}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{y}$ (2)
 > $\mathrm{Lineint}\left(f\left(x,y\right),x=t,y={t}^{2}\right)$
 ${∫}{f}{}\left({t}{,}{{t}}^{{2}}\right){}\sqrt{{\left(\frac{{ⅆ}}{{ⅆ}{t}}{}{t}\right)}^{{2}}{+}{\left(\frac{{ⅆ}}{{ⅆ}{t}}{}\left({{t}}^{{2}}\right)\right)}^{{2}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{t}$ (3)
 > $\mathrm{Lineint}\left(f\left(x,y\right),x,y,t=a..b\right)$
 ${{∫}}_{{a}}^{{b}}{f}{}\left({x}{}\left({t}\right){,}{y}{}\left({t}\right)\right){}\sqrt{{\left(\frac{{ⅆ}}{{ⅆ}{t}}{}{x}{}\left({t}\right)\right)}^{{2}}{+}{\left(\frac{{ⅆ}}{{ⅆ}{t}}{}{y}{}\left({t}\right)\right)}^{{2}}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{t}$ (4)