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Benedict Irwin edited Explaination.tex
over 9 years ago
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Where for the class of functions $x^ne^{-x}$ , $[xf(x)]_{-\infty}^\infty$ will always vanish.
This way any analogous scenario for the derivative of a sum, should follw the summation by parts, or Abel summation formula.
We can keep applying the same concept such that \begin{equation}
\int_a^b f(x) \;dx= C \\
\int_a^b xf'(x) \;dx = -C + [xf(x)]_a^b \\
\int_a^b xf'(x)+x^2f''(x) \;dx = C - [xf(x)]_a^b + [x^2f'(x)]_a^b \\
\int_a^b x^2f''(x)\;dx= 2C - 2[xf(x)]_a^b + [x^2f'(x)]_a^b
\end{equation}