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Forums
Mathematics
Calculus
Derivative and integral of the exponential e^t
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[QUOTE="PeroK, post: 6250460, member: 493650"] Yes, an indefinite integral produces an equivalence class of functions, not a unique function. This is important as you can see from the following example. We want to find functions, ##f(t)## that satisfy ##f''(t) = e^t##. Clearly ##f(t) = e^t## is one such function. But, ##f(t) = e^t + At + B## is also a solution to this differential equation, where ##A, B## are any two constants. Another way to look at this is to say that if you integrate ##f''(t) = e^t## you do not get a unique result. Differentiation, on the other hand, always gives a unique function as a result. [/QUOTE]
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Forums
Mathematics
Calculus
Derivative and integral of the exponential e^t
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