Calculate the moment of inertia if the area described in QUESTION 5.3.1 above rotates about the y-axis.

Step 1: Calculate the points of intersection for 5.1.1.
To find the points of intersection, set the two equations equal to each other:

$$3x - 2x^2 = \frac{1}{2}x$$

Multiply by 2 to clear the fraction:

$$6x - 4x^2 = x$$

Rearrange the terms to form a quadratic equation:

$$4x^2 - 5x = 0$$

Factor out $x$:

$$x(4x - 5) = 0$$

This gives two possible values for $x$:

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