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## Homework Statement

Determine the moment of inertia of the shaded area about the x-axis.

## Homework Equations

I(x)= y^2dA

## The Attempt at a Solution

In order to determine the moment of inertia of the shaded area about the x-axis I first looked at the portion above the x-axis, integrate it with a small rectangular element and then because of the symmetry I would multiply it with 2. So:

Yet if I integrate that with those limits and then multiply it with 2 and insert B= a/2

I do not get (a-sin (a))(r^4)/8. The answer I would get if I just use ∫∫((r*sinθ)^2)rdθdr. Which is the correct answer.

But why doesn't it work?