Finding Areas Between Curves with Maple

Now that you know how to plot more than one curve with Maple, let's try and find the area of intersection between two curves. For example, what is the area enclosed by the intersection of r = sin(t) and r = sin(3t)?

> with(plots):

>

> polarplot([sin(t),sin(3*t)],t=0..2*Pi);

How can you find the intersection points? Let's do this by hand first (which will be challenging!) and then verify using

> solve(sin(t)=sin(3*t));

>

Next, we just subtract areas. Again let's do this by hand and then verify by using:

> (int(0.5*(sin(3*t))^2-0.5*sin(t)^2,t=0..Pi/4));

>