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Benedict Irwin edited Explaination.tex
over 9 years ago
Commit id: 9858c42eae29232fc09fdc37bd1243fd537d6be2
deletions | additions
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index 60bfb73..663fb02 100644
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\int_a^b x^2f''(x)\;dx= 2C - 2[xf(x)]_a^b + [x^2f'(x)]_a^b \\
\int_a^b 2x^2f''(x) + x^3f'''(x) \;dx = -2C +2[xf(x)]_a^b -[x^2f'(x)]_a^b +[x^3f''(x)]_a^b \\
\int_a^b x^3f'''(x) \;dx = -6C +6[xf(x)]_a^b -3[x^2f'(x)]_a^b +[x^3f''(x)]_a^b
\end{equation}
This progression continiues and one can fins that \begin{equation}
\int_a^b x^nf^{(n)} \;dx = \sum_{k=0}^n \frac{(-1)^k}{k!}(-1)^nn!B_n
\end{equation}
Where $B_0=C$ and $B_i=[x^if^{(i-1)}]_a^b$.