The next problem involves evaluating the following iterated double integral:

$\int_{1}^{6} \left( \int_{0}^{6} \frac{1}{4} x^5 y \, dx \right) dy$

Steps to Solve:

1. Inner Integral: Solve the inner integral first, which is with respect to $x$: $\int_{0}^{6} \frac{1}{4} x^5 y \, dx$ Since $y$ is treated as a constant, factor out $\frac{y}{4}$, and focus on integrating $x^5$: $\frac{y}{4} \int_{0}^{6} x^5 \, dx$ The integral of $x^5$ is: $\frac{x^6}{6}$ Now, evaluate this from $x = 0$ to $x = 6$: [ \frac{y}{4} \cdot \left( \frac{6^6}{6} - \frac{0^6}{