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Home » \( 500 \times 0.343 = 171.5 \) - DNSFLEX

\( 500 \times 0.343 = 171.5 \) - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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\int_0^1 \int_0^{\min(0.2, 1 - u)} 30 s^4 \, ds \, du
Split into two regions: $ 0 \leq u \leq 0.8 $, where $ 1 - u \geq 0.2...
= \int_0^{0.8} \int_0^{0.2} 30 s^4 ds \, du + \int_{0.8}^1 \int_0^{1 -...
First integral:
\int_0^{0.2} 30 \cdot \frac{s^5}{5} ds = 6 \int_0^{0.2} s^5 ds = 6 \cd...
Multiply by 1 (no outer u): $ \frac{1}{15625} $
Second integral:
\int_{0.8}^1 30 \cdot \frac{(1 - u)^5}{5} du = 6 \int_{0.8}^1 (1 - u)^...
Let $ w = 1 - u $, $ dw = -du $, limits $ w = 0.2 $ to $ 0 $:
\int_0^{0.2} w^5 dw = 6 \cdot \frac{w^6}{6} \Big|_0^{0.2} = (0.2)^6 =...

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