If the domain of definition of the integral does not include 0, it is still possible for the integral to be integrable. The integrability of the integral depends on the function being integrated and the behavior of the function within its domain. Excluding 0 from the domain does not automatically make the integral non-integrable; it is possible for the integral to be integrable over a restricted domain that does not include 0. **

An integrable function is a function that can be integrated over a given interval to produce a finite result. In other words, the area under the curve of the function is well-defined and does not approach infinity. Mathematically, a function f(x) is integrable on an interval [a, b] if the definite integral of f(x) over [a, b] exists and is finite. This concept is important in calculus and real analysis, as it allows for the calculation of areas, volumes, and other quantities using the techniques of integration. **

The integral is still integrable if the domain of definition does not include 0. The integrability of a function is determined by its behavior within the domain of integration, not by the presence of a specific value such as 0. Therefore, the integral can still be evaluated as long as the function is continuous and bounded within the given domain. Including 0 in the domain of definition does not automatically make the integral non-integrable; it depends on the behavior of the function at that specific point. **

No, a function does not have to be continuous to be integrable. A function can be integrable as long as it is bounded and has a finite number of discontinuities. For example, the function f(x) = 1/x is not continuous at x = 0, but it is integrable over the interval [1, 2]. The Riemann integral can still be defined for functions with a finite number of discontinuities, allowing them to be integrable. **

Acrylic paint is generally considered non-toxic for birds when fully dried and cured. It is important to ensure that the paint is labeled as non-toxic and safe for use around animals. Additionally, it is recommended to allow the paint to fully dry and cure before introducing it to the bird's environment to minimize any potential risks. **

When choosing paint for parrot cages, it is important to select a non-toxic option to ensure the safety of the birds. Look for paints that are specifically labeled as non-toxic and safe for use on bird cages. Water-based acrylic paints are a good choice as they are generally non-toxic and safe for birds. It is important to allow the paint to fully dry and air out before placing the birds back in the cage to ensure their safety. **

It is generally not advisable to paint non-woven wallpaper with latex paint. Non-woven wallpaper is designed to be breathable and moisture-resistant, which can make it difficult for latex paint to adhere properly. Additionally, painting non-woven wallpaper can alter its texture and appearance, potentially ruining the original design. It is recommended to consult with a professional or the wallpaper manufacturer for the best painting options for non-woven wallpaper. **

It is generally not recommended to paint non-woven wallpaper with latex paint. Non-woven wallpaper is designed to be breathable and painting it with latex paint can hinder its ability to breathe, potentially causing issues like peeling or bubbling. It is best to consult the manufacturer's recommendations or test a small inconspicuous area before painting non-woven wallpaper. If you do decide to paint it, consider using a primer specifically designed for non-woven wallpaper to ensure better adhesion and longevity of the paint. **