Area Between Two Curves

Computing

>	with(plots):

Warning, the name changecoords has been redefined

>	f1:=6+sin(Pi*x);

>	f2:=x^2-4*x+6;

>	f1Graph:=plot(f1,x=-2..6,y=0..10,thickness=2,color=red):

>	f2Graph:=plot(f2,x=-2..6,y=0..10,thickness=2,color=blue):

>	display(f1Graph,f2Graph);

>	fsolve({f1=f2},{x},x=-1..1);

>	fsolve({f1=f2},{x},x=3..5);

>	eval(f1,x=0);

>	eval(f1,x=4);

The graphs of the two functions intersect at (0,6) and (4,6).

The area between the two curves is given by the integral below.

>	Int(f1-f2,x=0..4);

>

value(%);

Below we do some coloring just for fun.

>	f1Graph2:=plot(f1,x=0..4,thickness=2,color=red,filled=true):

>	f2Graph2:=plot(f2,x=0..4,thickness=2,color=blue,filled=true):

>	display(f1Graph2);

>	display(f2Graph2);

>	display(f2Graph2,f1Graph2);

>	f2Graph3:=plot(f2,x=0..4,thickness=2,color=white,filled=true):

>	display(f2Graph3,f1Graph2);

>