GetIntegrand - Maple Help

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IntegrationTools

 GetIntegrand
 extract the integrand from an integral
 GetRange
 extract the range from a definite integral
 GetVariable
 extract the variable of integration from an integral
 GetOptions
 extract the option of integration from an integral
 GetParts
 extract the parts of an integral as a list

 Calling Sequence GetIntegrand(v) GetRange(v) GetVariable(v) GetOptions(v) GetParts(v)

Parameters

 v - definite or indefinite integral

Description

 • The GetIntegrand command extracts the integrand from a definite or indefinite integral.
 • The GetRange command extracts the range(s) from a definite integral.
 • The GetVariable command extracts the variable(s) of integration from a definite or indefinite integral.
 • The GetOptions command extracts any optional arguments from a definite integral.
 • The GetParts command extracts all of the above parts as a list [Integrand, [Variable(s)], [Range(s)], [Option(s)]].

Examples

 > $\mathrm{with}\left(\mathrm{IntegrationTools}\right):$
 > $v≔\mathrm{Int}\left(f\left({x}^{2}\right),x=a..b\right)$
 ${v}{≔}{{\int }}_{{a}}^{{b}}{f}{}\left({{x}}^{{2}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}$ (1)
 > $\mathrm{GetIntegrand}\left(v\right)$
 ${f}{}\left({{x}}^{{2}}\right)$ (2)
 > $\mathrm{GetRange}\left(v\right)$
 ${a}{..}{b}$ (3)
 > $\mathrm{GetVariable}\left(v\right)$
 ${x}$ (4)
 > $v≔\mathrm{Int}\left(f\left({x}^{2}\right),x\right)$
 ${v}{≔}{\int }{f}{}\left({{x}}^{{2}}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}$ (5)
 > $\mathrm{GetIntegrand}\left(v\right)$
 ${f}{}\left({{x}}^{{2}}\right)$ (6)
 > $\mathrm{GetVariable}\left(v\right)$
 ${x}$ (7)
 > $\mathrm{GetRange}\left(v\right)$
 > $\mathrm{GetParts}\left(v\right)$
 $\left[{f}{}\left({{x}}^{{2}}\right){,}\left[{x}\right]{,}\left[\right]{,}\left[\right]\right]$ (8)

Here is an example of a nested integral.

 > $w≔\mathrm{Int}\left(\mathrm{Int}\left(f\left(x,y\right),x=a..b\right),y=c..d\right)$
 ${w}{≔}{\mathrm{Typesetting}}{:-}{\mathrm{_Hold}}{}\left(\left[{\mathrm{Int}}{}\left({\mathrm{Int}}{}\left({f}{}\left({x}{,}{y}\right){,}{x}{=}{a}{..}{b}\right){,}{y}{=}{c}{..}{d}\right)\right]\right)$ (9)
 > $\mathrm{GetIntegrand}\left(w\right)$
 ${{\int }}_{{a}}^{{b}}{f}{}\left({x}{,}{y}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}$ (10)
 > $\mathrm{GetVariable}\left(w\right)$
 ${y}$ (11)
 > $\mathrm{GetParts}\left(w\right)$
 $\left[{{\int }}_{{a}}^{{b}}{f}{}\left({x}{,}{y}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}{,}\left[{y}\right]{,}\left[{c}{..}{d}\right]{,}\left[\right]\right]$ (12)

The same example given as a multiple integral.

 > $\mathrm{ww}≔\mathrm{Int}\left(f\left(x,y\right),\left[x=a..b,y=c..d\right]\right)$
 ${\mathrm{ww}}{≔}{\mathrm{Typesetting}}{:-}{\mathrm{_Hold}}{}\left(\left[{\mathrm{Int}}{}\left({f}{}\left({x}{,}{y}\right){,}\left[{x}{=}{a}{..}{b}{,}{y}{=}{c}{..}{d}\right]\right)\right]\right)$ (13)
 > $\mathrm{GetIntegrand}\left(\mathrm{ww}\right)$
 ${f}{}\left({x}{,}{y}\right)$ (14)
 > $\mathrm{GetVariable}\left(\mathrm{ww}\right)$
 ${x}{,}{y}$ (15)
 > $\mathrm{GetParts}\left(\mathrm{ww}\right)$
 $\left[{f}{}\left({x}{,}{y}\right){,}\left[{x}{,}{y}\right]{,}\left[{a}{..}{b}{,}{c}{..}{d}\right]{,}\left[\right]\right]$ (16)
 > $\mathrm{GetVariable}\left(\mathrm{sin}\left(x\right)\right)$
 > $\mathrm{GetOptions}\left(\mathrm{Int}\left(f\left(x\right),x=0..1,'\mathrm{continuous}'\right)\right)$
 ${\mathrm{continuous}}$ (17)

 See Also