Benedict Irwin edited Explaination.tex  over 9 years ago

Commit id: 33cc305909209f01bde2378e1e313765ff8a0c76

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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}