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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}{

Evaluate the iterated integral: ∫ from 1 to 6 ( ∫ from 0 to 6 (1/4 * x^5 * y) dx ) dy

Learn how to solve the iterated double integral ∫ from 1 to 6 ( ∫ from 0 to 6 (1/4 * x^5 * y) dx ) dy using step-by-step integration techniques. This problem covers double integration concepts and the fundamental theorem of calculus. Suitable for college-level calculus students.

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