Two Equal Areas

J.Osborne

> restart:with(plots):

It should be noted that, at least when is positive, the substitution technique shows how the area under one curve can be calculated as the area under a simpler curve. That is, for example, the area under above is equal to the area under above . In other words: .

> f:=x->cos(2*x/3);g:=u->3/2*cos(u);

> Int(f(x),x=0..Pi/2):%=value(%);Int(g(u),u=0..Pi/3):%=value(%);

> P1:=plot([f(x),g(x)],x=0..Pi/2,y=0..3/2,thickness=3,colour=[blue,red]):

> P2:=seq(plot([k*Pi/80,t,t=0..f(k*Pi/80)],colour=blue),k=1..40):

> P3:=seq(plot([k*Pi/150,t,t=0..g(k*Pi/150)],colour=red),k=1..50):

> display(P1,P2,P3);