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Examples offundamental theorem of calculus
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The value of the final integral thus follows from thefundamentaltheoremofcalculus.
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Furthermore, when evaluating definite integrals using thefundamentaltheoremofcalculus, the constant will always cancel with itself.
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This example is from Wikipedia and may be reused under a CC BY-SA license.This is another formulation of thefundamentaltheoremofcalculus.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Thefundamentaltheoremofcalculusstates that antidifferentiation is the same as integration.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The usualfundamentaltheoremofcalculusfor single-variable calculus has the following local generalization.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In effect, thefundamentaltheoremofcalculuswas built into his calculations.
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This example is from Wikipedia and may be reused under a CC BY-SA license.It may be seen as a stochastic generalization of the (second)fundamentaltheoremofcalculus.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Integration by substitution can be derived from thefundamentaltheoremofcalculusas follows.
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This example is from Wikipedia and may be reused under a CC BY-SA license.This is a consequence of thefundamentaltheoremofcalculusand the fact that derivative of ln ("x") is 1/ "x".
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This example is from Wikipedia and may be reused under a CC BY-SA license.In particular, thefundamentaltheoremofcalculusallows one to solve a much broader class of problems.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Thefundamentaltheoremofcalculusestablishes the relationship between indefinite and definite integrals and introduces a technique for evaluating definite integrals.
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This example is from Wikipedia and may be reused under a CC BY-SA license.For most integrands we can't use thefundamentaltheoremofcalculusto compute the integral analytically; we have to approximate it numerically.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Using thefundamentaltheoremofcalculusoften requires finding an antiderivative.
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This example is from Wikipedia and may be reused under a CC BY-SA license.In one dimension, it is equivalent to thefundamentaltheoremofcalculus.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Thus, in the case that is a 0-form and is a closed interval of the real line, this reduces to thefundamentaltheoremofcalculus.
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This example is from Wikipedia and may be reused under a CC BY-SA license.For example, thefundamentaltheoremofcalculusgives the relationship between differential calculus and integral calculus, which are two distinct branches that were not obviously related.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The first part of the theorem, sometimes called the firstfundamentaltheoremofcalculus, is that an indefinite integral of a function can be reversed by differentiation.
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This example is from Wikipedia and may be reused under a CC BY-SA license.It is a generalization of thefundamentaltheoremofcalculusto any curve in a plane or space (generally "n" -dimensional) rather than just the real line.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Barrow provided the first proof of thefundamentaltheoremofcalculus.
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This example is from Wikipedia and may be reused under a CC BY-SA license.This is shown from the binomial formula and the definition of the derivative and thus by thefundamentaltheoremofcalculusthe antiderivative is the integral.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.