Permachart - Marketing Reference Guide: Iterated Integral, Centroid, Multiple Integral

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Tm integral calculus theorems types of integrals average value theorem: if f(x) is continuous over [a,b], then b. 1 a f x f x dx y which means that the integral a equals the area of the rectangle a f x a y y = f(x) f(x) a x b. Fundamental theorems: if f is continuous on [a, b], then. F x f t dt x a d dx means x a f t dt f x (that is, f is the anti-derivative of f: if f is the anti-derivative of f, then b a f x dx. Function: if f(x) = continuous over [a, b], then y x y s b a b a a ydx b dx yds b ds a. = average ordinate with respect to abscissa x over [a,b] = average ordinate with respect to arc length s over [a,b] i s.

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