\( \int \beta y ^ { 2 } \)

To find the integral of \( \beta y^2 \) with respect to \( y \), you'll apply the power rule of integration. The integral becomes \( \frac{\beta}{3} y^3 + C \), where \( C \) is the constant of integration. So, you're essentially scaling the \( y^2 \) term up into a \( y^3 \) term and taking care of that coefficient! When integrating, it's important to remember that \( \beta \) acts as a constant during the process. So if you have multiple variables or functions later on, you'll want to keep track of that juggling act! For instance, make sure not to confuse \( \beta \) with any variable limits of integration should you decide to venture into definite integrals. Integration can be a delightful dance through the world of functions!