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## Homework Statement

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

The curve is represented by y

^{2}=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}= ∫x

^{2}dA.

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}= ∫x

^{2}ydx.

I substituded (2-/sqrt(2x)) for y and solved for the integral from (0<x<2)

My answer I got was 2.13m

^{4}and the answer is incorrect.

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