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Proof of: ∫ f(x) + g(x) dx = ∫ f(x) dx + ∫g(x) dx
It is also a very easy proof. Assume that F(x) is an anti-derivative of f(x) and that G(x) is an anti-derivative of g(x). Therefore we have that F′(x) = f(x) and G′(x) = g(x).
Fundamental properties of derivatives also give us that
(F(x) + G(x))' = F'(x) + G(x) = f(x) + g(x)
and thus F(x) + G(x) is an anti-derivative of f(x) + g(x) and F(x) - G(x) is an anti- derivative of f(x)- g(x). So,
∫ f(x) + g(x) dx = F(x) + G(x) + c =∫ f(x) dx + ∫g(x) dx
New England University maintains a data warehouse that stores information about students, courses, and instructors. Members of the university's Board of Trustees are very much inte
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Rules for Partial Derivatives For a function, f = g (x, y) . h (x, y) = g (x, y) + h
if a,b,c are in HP
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