Home / \int_{0.8}^1 30 \cdot \frac{(1 - u)^5}{5} du = 6 \int_{0.8}^1 (1 - u)^5 du

\int_{0.8}^1 30 \cdot \frac{(1 - u)^5}{5} du = 6 \int_{0.8}^1 (1 - u)^5 du

February 22, 2026

$\int_{0.8}^1 30 \cdot \frac{(1 - u)^5}{5} du = 6 \int_{0.8}^1 (1 - u)^5 du$

\int_0^{0.2} 30 \cdot \frac{s^5}{5} ds = 6 \int_0^{0.2} s^5 ds = 6 \cdot \frac{s^6}{6} \Big|_0^{0.2} = (0.2)^6 = \left(\frac{1}{5}\right)^6 = \frac{1}{15625}
Multiply by 1 (no outer u): $ \frac{1}{15625} $
Second integral:
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 = \frac{1}{15625}
Total: $ \frac{1}{15625} + \frac{1}{15625} = \frac{2}{15625} $