Volume of a Solid

Picture and Computation

with(plots):

Warning, the name changecoords has been redefined

The Base

>	Bottom:=plot([t,t^2-4,t=-2..3],thickness=3,labels=[x,y]):

>	Top:=plot([t,t+2,t=-2..3],thickness=3,labels=[x,y]):

>	display(Bottom,Top);

The Solid

>	plot3d(4+x^2+2*y^2,x=-2..3,y=x^2-4..x+2,filled=true,axes=boxed,orientation=[145,45]);

Computing the Volume

>	Int(Int(4+x^2+2*y^2,y=x^2-4..x+2),x=-2..3);

>

value(%);

>

evalf(%);

>