Question: User: $\int\int$ $$$\sum_{i=1}^ni^2$ (x²+y)
1. **Problem Statement:**
Calculate the double integral of the function $$\sum_{i=1}^n i^2 (x^2 + y)$$ over a given region.
2. **Understanding the expression:**
The summation $$\sum_{i=1}^n i^2$$ is a constant with respect to variables $x$ and $y$.
3. **Formula for the summation:**
$$\sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$$
4. **Rewrite the integral:**
The integral becomes:
$$\int \int \left( \frac{n(n+1)(2n+1)}{6} \right) (x^2 + y) \, dx \, dy$$
5. **Factor out the constant:**
$$\frac{n(n+1)(2n+1)}{6} \int \int (x^2 + y) \, dx \, dy$$
6. **Next steps:**
To proceed, the limits of integration or the region of integration must be specified.
7. **Summary:**
- Calculate the summation using the formula.
- Multiply by the integral of $(x^2 + y)$ over the specified region.
Without limits, the integral cannot be evaluated further.