MATH 1080 Lecture Notes - Lecture 19: Antiderivative, Inverse Function, Xu
19 Nov 2017
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Page 251: finding the reverse of the derivative by giving the function and finding the original, f"(x) = f(x) Fx (x2 + 2) = 2x + 0. * it does not matter whether it is arbitrary or not. Find the derivative for 2x: find big f, f" (x) = 2x, above we said that x2 + c, f(x) f(x) + c, such that f"(x) = f(x) Definition f(x) is an antiderivative integral of f(x) if f"(x) =f(x) If you take the inverse function of the derivative you get the antiderivative plus a constant: the first one says take the antiderivative of f, you play most with the integrand f(x, dx is known as the differential. If you take the antiderivative of f you still get a f which is another function. The derivative of the antiderivative you are doing nothing. It is just f are shown on the page. Dx (ff(x)dx) dx (f(x) + c f" (x) + c f(x)
