student(deprecated)/Tripleint - Maple Help

student

 Tripleint
 inert form of triple integration

 Calling Sequence Tripleint(g, x, y, z) Tripleint(g, x, y, z, Domain) Tripleint(g, x = a..b, z = e..f, y = c..d)

Parameters

 g - expression to be integrated x, y, z - variables of integration a, b, c, d, e, f - (optional) lower and upper bounds defining the range of integration Domain - (optional) name identifying the region of integration

Description

 • Important: The student package has been deprecated. Use the superseding command Student[MultivariateCalculus][MultiInt] instead.
 • This function corresponds to a triple integral of g with respect to x, y, and z. It uses an unevaluated form of the Maple int function, so only minor simplifications are performed.
 • For definite integration, a range of integration (x = a..b) must be indicated for each integration variable.
 • Alternatively you may use a name to indicate the entire region of integration. This latter form is strictly notational and cannot be evaluated.
 • Use value to force Tripleint to evaluate like int. The inner Doubleint can be evaluated by using map(value,...)

Examples

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

 > $\mathrm{with}\left(\mathrm{student}\right):$
 > $\mathrm{Tripleint}\left(g\left(x,y,z\right),x,y,z\right)$
 ${\int }\left({\int }\left({\int }{g}{}\left({x}{,}{y}{,}{z}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{y}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{z}$ (1)
 > $\mathrm{Tripleint}\left(hg,x=1..n,y=2..4,z=a..b\right)$
 ${{\int }}_{{a}}^{{b}}\left({{\int }}_{{2}}^{{4}}\left({{\int }}_{{1}}^{{n}}{h}{}{g}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{y}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{z}$ (2)
 > $\mathrm{Tripleint}\left(hg,x,y,z,C\right)$
 ${{\int }}_{{}}^{{}}\left({{\int }}_{{}}^{{}}\left({{\int }}_{{C}}^{{}}{h}{}{g}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{y}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{z}$ (3)