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To set up the integral for the area moment of inertia about the y-axis ($I_y$) using a vertical strip, express the differential area $dA$ as the product of the strip's height (upper boundary minus lower boundary) and its width $dx$. Substitute this into the definition $I_y = \int x^2 dA$ and determine the integration limits based on the horizontal extent of the region bounded by functions of $x$.

Conditions: The region is bounded by curves that can be expressed as functions of $x$.; A vertical differential strip is chosen, meaning its width is $dx$.; The integration variable is $x$.

To set up the integral for the area moment of inertia about the y-axis ($I_y$) using a vertical strip, express the differential area $dA$ as the product of the strip's height (upper boundary minus lower boundary) and its width $dx$. Substitute this into the definition $I_y = \int x^2 dA$ and determine the integration limits based on the horizontal extent of the region bounded by functions of $x$.

Conditions: The region is bounded by curves that can be expressed as functions of $x$.; A vertical differential strip is chosen, meaning its width is $dx$.; The integration variable is $x$.