If df(x)/dx = g(x), then integral [from a to b] g(x) dx = f(b)-f(a).
In plain English: the definite integral can be calculated by finding the antiderivative, evaluating it at the endpoints, and subtracting.
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He is responsible for the FTC, or fundamental theorem of calculus.
there was no sure answer about who started calculus but it was Isaac Newton and Gottfried Wilhelm Leibniz who founded calculus because of their fundamental theorem of calculus.
We need more information. Is there a limit or integral? The theorem states that the deivitive of an integral of a function is the function
I don't know the details about this particular student, but I would hazard a guess that he didn't know quite a few other things about calculus, either. In any case, if you don't know the fundamental theorem - at least, if you don't know how to apply it in practice - you'll have serious problems with many different problems - specifically when you need to do definite integrals.
The fundamental theorum of calculus states that a definite integral from a to b is equivalent to the antiderivative's expression of b minus the antiderivative expression of a.