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İngilizce
It is a generalization of the fundamental theorem of calculus to any curve in a plane or space (generally "n" -dimensional) rather than just the real line.
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This is shown from the binomial formula and the definition of the derivative and thus by the fundamental theorem of calculus the antiderivative is the integral.
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Thus, in the case that is a 0-form and is a closed interval of the real line, this reduces to the fundamental theorem of calculus.
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It may be seen as a stochastic generalization of the (second) fundamental theorem of calculus.
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Integration by substitution can be derived from the fundamental theorem of calculus as follows.
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In particular, the fundamental theorem of calculus allows one to solve a much broader class of problems.
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For most integrands we can't use the fundamental theorem of calculus to compute the integral analytically; we have to approximate it numerically.
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Barrow provided the first proof of the fundamental theorem of calculus.
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Using the fundamental theorem of calculus often requires finding an antiderivative.
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The fundamental theorem of calculus states that antidifferentiation is the same as integration.
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