Along with giving us a technique to compute antiderivatives, integration by parts is very important theoretically. In this context, it can be thought of as a technique for moving derivatives off of one function and onto another. To see what we mean, suppose that f(x) and g(x) are functions with f(0) = g(0) = 0, f(1) = g(1) = 0 and with continuous second derivatives f’’(x) and g’’(x). Use integration by parts twice to show that the integral from [0,1] of f''(x)g(x) dx = the integral from [0,1] of f(x)g''(x) dx..
This question was answered on: Sep 21, 2023
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