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To set up the integral for $I_y$ using a vertical strip, first express the differential area $dA$ in terms of $x$. A vertical strip has an infinitesimal width $dx$ and a height determined by the difference between the upper and lower boundary curves at position $x$.

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 $I_y$ using a vertical strip, first express the differential area $dA$ in terms of $x$. A vertical strip has an infinitesimal width $dx$ and a height determined by the difference between the upper and lower boundary curves at position $x$.

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 $x$.

The indefinite integral is simply another name for the antiderivative. Both terms refer to the family of functions whose derivative is the given function, typically expressed with an arbitrary constant $C$.

Conditions: The context is introductory calculus focusing on reverse differentiation.; The function is continuous or differentiable on the interval of interest.

The indefinite integral is simply another name for the antiderivative. Both terms refer to the family of functions whose derivative is the given function, typically expressed with an arbitrary constant $C$.

Conditions: The context is introductory calculus focusing on reverse differentiation.; The function is continuous or differentiable on the interval of interest.

The notation $\int 2x \, dx$ is a compact way to ask for the antiderivative of $2x$ with respect to $x$. It represents the entire family of functions whose derivative is $2x$, which is written as $x^2+C$.

Conditions: The variable of integration is $x$.; The integrand is $2x$.

The notation $\int 2x \, dx$ is a compact way to ask for the antiderivative of $2x$ with respect to $x$. It represents the entire family of functions whose derivative is $2x$, which is written as $x^2+C$.

Conditions: The variable of integration is $x$.; The integrand is $2x$.