![]() The observations made in the preceding two paragraphs demonstrate that differentiating and integrating (where we integrate from a constant up to a variable) are almost inverse processes. At right, the antiderivative function \(F(x) = \frac\) At left, the graph of \(f(x) = x^2\) on the interval \(\) and the area it bounds. If the definite integral represents an accumulation function, then we find what is sometimes referred to as the Second Fundamental Theorem of Calculus: In other words, the derivative of a simple accumulation function gets us back to the integrand, with just a change of variables(recall that we use t in the integral to distinguish it from the x i.
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