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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
use the distributive law to write each multiplication in a different way. the find the answer. 12x14 16x13 14x18 9x108 12x136 20x147
can i known the all equations under this lesson with explanations n examples. please..
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how do you differentiate sinx/ex?
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