4.9: Antiderivatives
For each of the following functions, find all antiderivatives. f(x) = 3x2 f(x) = 1 x f(x) = cosx f(x) = ex Solution: a. Because d dx(x3) = 3x2 then F(x)
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To find the antiderivative of scalar multiple of a function f (x), we can find it using the formula given by, ∫kf (x) dx = k ∫f (x) dx. This implies, the antidifferentiation of kf (x) is equal to k times
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Example: Finding Antiderivatives f (x) = 3x2 f ( x) = 3 x 2 f (x) = 1 x f ( x) = 1 x f (x) = cosx f ( x) = cos x f (x) = ex f ( x) = e x
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