Integrais triples $\int_{x_1}^{x_2} \int_{y_1}^{y_2} \int_{z_1}^{z_2}f(x,y,z) dz dy dx$
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#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,xymin,yzmin,z0:
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('