You can skip the parallel axis theorem when the problem asks for the area moment of inertia directly about one of the coordinate axes used in the integral setup, provided there is no perpendicular offset distance to account for. In the specific example shown, the goal is to find about the y-axis itself.
Conditions: The requested axis is one of the coordinate axes (e.g., the x-axis or y-axis).; The integral is set up directly about that same axis.; No separate shifted-axis correction is being applied in the setup.
You can skip the parallel axis theorem when the problem asks for the area moment of inertia directly about one of the coordinate axes used in the integral setup, provided there is no perpendicular offset distance to account for. In the specific example shown, the goal is to find about the y-axis itself.
Conditions: The requested axis is one of the coordinate axes (e.g., the x-axis or y-axis).; The integral is set up directly about that same axis.; No separate shifted-axis correction is being applied in the setup.