@Integrais triples
system:sage


<CENTER>
<HR>
<H3>Integrais triples $\int_{x_1}^{x_2} \int_{y_1}^{y_2} \int_{z_1}^{z_2}f(x,y,z) dz dy dx$</H3>
</CENTER>

{{{id=0|
#auto
%hide
var('x,y,z')
def vv(t):
  if t in RR:
      a=(t,)
  else:
      a=t.variables()
  return a
@interact
def example(f=x^2*sin(z), rango_x='(0,pi)', rango_y='(0,x)', rango_z='(0,x*y)', update=selector(['Update'],buttons =True, label='')):
    assumptions='[]'
    xmin, xmax = sage_eval(rango_x,locals={'y':y,'z':z});
    ymin, ymax = sage_eval(rango_y,locals={'x':x,'z':z});
    zmin, zmax = sage_eval(rango_z,locals={'x':x,'y':y});
    ass=sage_eval(assumptions,locals={'x':x,'y':y,'z':z});
    forget()
    ass=[x>xmin,x<xmax,y>ymin,y<ymax,z>zmin,z<zmax]
    if len(ass)>0:
        for i in range(len(ass)):
            assume(ass[i])
    if xmin in RR and xmax in RR:
        if ymin in RR and ymax in RR:
            R=integral(integral(integral(f,z,zmin,zmax),y,ymin,ymax),x,xmin,xmax)
        else:
            if (not(z in vv(ymin)) and not(z in vv(ymax))):
                R=integral(integral(integral(f,z,zmin,zmax),y,ymin,ymax),x,xmin,xmax)
            else:
                R=integral(integral(integral(f,y,ymin,ymax),z,zmin,zmax),x,xmin,xmax)
    if ymin in RR and ymax in RR:
        if xmin in RR and xmax in RR:
            R=integral(integral(integral(f,z,zmin,zmax),y,ymin,ymax),x,xmin,xmax)
        else:
            if (not(z in vv(xmin)) and not(z in vv(xmax))):
                R=integral(integral(integral(f,z,zmin,zmax),x,xmin,xmax),y,ymin,ymax)
            else:
                R=integral(integral(integral(f,x,xmin,xmax),z,zmin,zmax),y,ymin,ymax)
    if zmin in RR and zmax in RR:
        if ymin in RR and ymax in RR:
            R=integral(integral(integral(f,x,xmin,xmax),y,ymin,ymax),z,zmin,zmax)
        else:
            if (not(x in vv(ymin)) and not(x in vv(ymax))):
                R=integral(integral(integral(f,x,xmin,xmax),y,ymin,ymax),z,zmin,zmax)
            else:
                R=integral(integral(integral(f,y,ymin,ymax),x,xmin,xmax),z,zmin,zmax)
    html('<h2>O valor da integral triple é $%s$</h2>'%latex(R))
    num=R.n(digits=6)
    html('<h2>Unha aproximación numérica é $%s$</h2>'%latex(num))
///
<html><!--notruncate--><div padding=6 id="div-interact-0"> <table width=800px height=20px bgcolor="#c5c5c5"
                 cellpadding=15><tr><td bgcolor="#f9f9f9" valign=top align=left><table><tr><td align=right><font color="black">f&nbsp;</font></td><td><input type="text" value="x^2*sin(z)" size=80 onchange="interact(0, '_interact_.update(\'0\', \'f\', 5, _interact_.standard_b64decode(\''+encode64(this.value)+'\'), globals()); _interact_.recompute(\'0\');')"></input></td></tr>
<tr><td align=right><font color="black">rango_x&nbsp;</font></td><td><input type="text" value="(0,pi)" size=80 onchange="interact(0, '_interact_.update(\'0\', \'rango_x\', 6, _interact_.standard_b64decode(\''+encode64(this.value)+'\'), globals()); _interact_.recompute(\'0\');')"></input></td></tr>
<tr><td align=right><font color="black">rango_y&nbsp;</font></td><td><input type="text" value="(0,x)" size=80 onchange="interact(0, '_interact_.update(\'0\', \'rango_y\', 7, _interact_.standard_b64decode(\''+encode64(this.value)+'\'), globals()); _interact_.recompute(\'0\');')"></input></td></tr>
<tr><td align=right><font color="black">rango_z&nbsp;</font></td><td><input type="text" value="(0,x*y)" size=80 onchange="interact(0, '_interact_.update(\'0\', \'rango_z\', 8, _interact_.standard_b64decode(\''+encode64(this.value)+'\'), globals()); _interact_.recompute(\'0\');')"></input></td></tr>
<tr><td colspan=2><table style="border:1px solid #dfdfdf; background-color:#efefef;">
<tr><td><button style="border-style:outset;" value="0" onclick="interact(0, '_interact_.update(\'0\', \'update\', 9, _interact_.standard_b64decode(\''+encode64(this.value)+'\'), globals()); _interact_.recompute(\'0\');')">Update</button>
</td></tr></table></td></tr>
</table><div id="cell-interact-0"><?__SAGE__START>
        <table border=0 bgcolor="white" width=100% height=100%>
        <tr><td bgcolor="white" align=left valign=top><pre><?__SAGE__TEXT></pre></td></tr>
        <tr><td  align=left valign=top><?__SAGE__HTML></td></tr>
        </table><?__SAGE__END></div></td>
                 </tr></table></div>
                 </html>
}}}

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///
}}}