Determine for the quarter ellipse of Prob. 9.67 the moments of inertia and the product of inertia with respect to new axes obtained by rotating the x and y axes about O (a) through 45° counterclockwise, (b) through 30° clockwise.

(Reference to Problem 9.67):

Determine by direct integration the product of inertia of the given area with respect to the x and y axes.

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