MapleAreaBetweenCurves.mws

Area Between Two Curves

An Approximation

>    with(plots): 

Warning, the name changecoords has been redefined

>    f1:=exp(1+x^2/3);

f1 := exp(1+1/3*x^2)

>    f2:=10-ln(x^2+3);

f2 := 10-ln(x^2+3)

>    f1Graph:=plot(f1,x=-2..2,y=0..12,thickness=2,color=red):

>    f2Graph:=plot(f2,x=-2..2,y=0..12,thickness=2,color=blue):

>    display(f1Graph,f2Graph);

[Maple Plot]

>    fsolve({f1=f2},{x},x=-2..-1);

{x = -1.815947859}

>    fsolve({f1=f2},{x},x=1..2);

{x = 1.815947859}

>    eval(f1,x=-1.815947859);

8.159820809

>    eval(f1,x=1.815947859);

8.159820809

The graphs of the two functions intersect at approximately (-1.815947859,8.159820809) and (1.815947859,8.159820809).

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

>    Int(f2-f1,x=-1.815947859..1.815947859);

Int(10-ln(x^2+3)-exp(1+1/3*x^2),x = -1.815947859 .. 1.815947859)

>    value(%);

16.21836906

>