For one of your issues, because defint needs integration limits to be
real, you have to tell Maxima that y is >0.
(%i2) integrate(integrate(x*y^2,x,y^(1/2),1),y,0,1);
defint: lower limit of integration must be real; found sqrt(y)
-- an error. To debug this try debugmode(true);
(%i3) assume(y>0);
(%o3) [y > 0]
(%i4) integrate(integrate(x*y^2,x,y^(1/2),1),y,0,1);
(%o4) 1/24
I cannot help you with plot.
Stefano
2009/12/19 Doug Edmunds (gmail) <dougedmunds at gmail.com>:
> I've been looking at Kahn Academy videos at
> www.khanacademy.org.
>
> In the Calculus videos on Double Integrals
> (videos 5 and 6),
> he works a problem for the area under a surface
> where the surface z = x*y^2 and y = x^2.
>
> He solves the area under z two ways, essentially:
>
> integrate(integrate(x*y^2,y,0,x^2),x,0,1);
> ?> 1/24
>
> integrate(integrate(x*y^2,x,y^(1/2),1),y,0,1);
> (Maxima can't do it this way)
>
> Is it possible to plot this problem using plot3d
> or something else?
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