Three identical balls, with masses M, 2M, and 3M are fastened to a massless rod of length L as shown. The rotational inertia about the left end of the rod is: That's the layout below. Would calculus be needed in this problem (intergration) because then Im in trouble. I know the rotation at the end of rod is I=ML^2/3. Could I use that formula.

3M-----L/2----2M----L/2-----M

It is not clear in what plane the rotation is. If the rod is not rotating about its axis, but in fact about a perpendicular through its left end, then just add the I for the outer two masses (1/2 mr^2) for each, and that makes the composite I. No, you don't need calculus. The formula you proposed is for a rod with mass.

I came up with an answer of 3ML^2/2
does that look right. Thanks