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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
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
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1+2cos(2x=0
A telephone company charges $.35 for the first minute of a phone call and $.15 for each additional minute of the call. Which of the subsequent represents the cost y of a phone call
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Using the same mean and standard deviation as mean m = 20.1 and a standard deviation s = 5.8. Joe was informed that he scored at the 68 th percentile on the ACT, what was Joe's ap
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RATIONAL NUMBERS All numbers of the type p/q where p and q are integer and q ≠0, are known as rational. Thus it can be noticed that every integer is a rational number
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