Moment of Inertia - Find Area Around Y-Axis

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This is my first time posting in this site so if I left out any information or the information needs to be formatted differently I apologize ahead of time.

Homework Statement

Determine the moment of inertia of the area about the y axis.

The curve is represented by y²=2x, and the shaded region is the smaller area above the curve.

0m<x<2m
0m<y<2m

Homework Equations

Is the parallel axis theorem needed? If it is, why is the reason?

The Attempt at a Solution

Since the problem asks for moment of Intertia about the y-axis

1. I_y= ∫x²dA.

2. I chose my dA to be xdy because I need to find a "bar" perpendicular to the axis I am trying to find the moment of inertia about.

3. Solved

I_y= ∫x²ydx.
I substituded (2-/sqrt(2x)) for y and solved for the integral from (0<x<2)

My answer I got was 2.13m⁴ and the answer is incorrect.

Is my process correct or do I need to find different limits of integration?

 

[Cheerios]

I don't know how to close a thread, I found out my error was in the integration process.

Solved, Iy= .762m^4.