> plot(x^2-4,x=-3..3);If you wanted to find the area created by the parabola and the x-axis you need to use the fact that the equation of the x axis is . Integrate the top function from the bottom with the limits of integration being the intersection points.

>int(0-x^2-4,x=-2..2);The next example shows how Maple can be used to find the intersection points and then use these to calculate the bounded area.

> f := x-> -x^2+4*x+6; > g := x-> x/3+2; > plot({f(x),g(x)},x=-2..6); > a := fsolve(f(x)=g(x),x=-2..0); > b := fsolve(f(x)=g(x),x=4..6); > int(f(x)-g(x),x=a..b);This final example shows how to break up the area if necessary. If you want to find the area bounded by the three graphs:

> f:=x->x+4;g:=x->-x+5;h:=x->sqrt(x^2+3); > plot({f(x),g(x),h(x)},x=-4..4,color=red);Notice that there are two functions that bound the top of the area. To find the complete area , break the problem into two. First find the area of and the square root and then find the area of and the square root. Then add these results. As usual you need to find the intersection points.

> solve(f(x)=g(x),x); > solve(f(x)=h(x),x); > solve(g(x)=h(x),x);Now do the

>evalf(int(f(x)-h(x),x=-13/8..1/2)+int(g(x)-h(x),x=1/2..11/5));

- Find the area bounded by the two functions
and
. First plot the two functions over the domain
.
- Find the area bounded by the three functions
,
and
. First create a plot that clearly shows the bounded area.
- Find the
**total**area bounded by the functions and . (Hint: there is more than one bounded region).

2006-03-23