fundamental theorem of calculus

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fundamental theorem of calculus

[¦fən·də¦ment·əl ¦thir·əm əv ′kal·kyə·ləs]
(mathematics)
Given a continuous function ƒ(x) on the closed interval [a,b ] the functional is differentiable on [a,b ] and F(x) = ƒ(x) for every x in [a,b ], and if G is any function on [a,b ] such that G ′(x) = ƒ(x) for all x in [a,b ], then
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The topics include integration using trigonometric identities, integration by parts, the fundamental theorems of calculus, applying the definite integral to compute the area of a plane figure, and methods of solving ordinary differential equations of the first order and of the first degree.

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