1. Area:

A= integral(x=-3:3) y dx = integral(x=-3:3) sqrt(9-x^2) dx

There are a number of ways of doing this integral, some of which you

should find in you calculus notes. The simplest is to observe that we are

trying to find the area of a semi-circle of radius 3, so the area is (9/2) pi.

2. and 3, I don't know what you want M sub x or M sub y to mean so I

cant help you.

4. mean of x:

mx = integral(R) x dR

where R is the region defined and dR is the element of area.

mx= integral(x=-3:3){integral(y=0:sqrt(9-x^2)) x dydx}.

But we can observe that by symmetry mean of x is zero.

5. Similarly: mean of y:

mx = integral(R) y dR

where R is the region defined and dR is the element of area.

mx= integral(x=-3:3){integral(y=0:sqrt(9-x^2)) y dydx}

RonL