@Integrais doble
system:sage


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<HR>
<H3>Integrais dobles $\int_{x_1}^{x_2} \int_{y_1}^{y_2} f(x,y) dy dx$</H3>
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#auto
%hide
var('x,y')
@interact
def example(f=y/(x^2+y^2), rango_x='(2, 4)', rango_y='(1/2,1)'):
    assumptions='[]'
    xmin, xmax = sage_eval(rango_x,locals={'y':y}); ymin, ymax = sage_eval(rango_y,locals={'x':x});
    ass=sage_eval(assumptions,locals={'x':x,'y':y});
    forget()
    if len(ass)>0:
        for i in range(len(ass)):
            assume(ass[i])
    if not (ymin in RR and ymax in RR):
        assume(x>xmin);assume(x<xmax);
        R=integral(integral(f,y,ymin,ymax),x,xmin,xmax)
    else:
        assume(y>ymin);assume(y<ymax);
        R=integral(integral(f,x,xmin,xmax),y,ymin,ymax)
    html('<h2>O valor da integral doble 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="y/(x^2 + y^2)" size=80 onchange='interact(0, "_interact_.update(0, \"f\", 1, _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="(2, 4)" size=80 onchange='interact(0, "_interact_.update(0, \"rango_x\", 2, _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="(1/2,1)" size=80 onchange='interact(0, "_interact_.update(0, \"rango_y\", 3, _interact_.standard_b64decode(\""+encode64(this.value)+"\"), globals());_interact_.recompute(0)")'></input></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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///
}}}