Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)f(x) = 7x + 4 cos xF(x) =
Question
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)f(x) = 7x + 4 cos xF(x) =
Solution
The most general antiderivative of the function f(x) = 7x + 4cos(x) is obtained by integrating each term separately.
The antiderivative of 7x is (7/2)x^2.
The antiderivative of 4cos(x) is 4sin(x).
Therefore, the most general antiderivative of the function is F(x) = (7/2)x^2 + 4sin(x) + C, where C is the constant of integration.
You can check this by differentiating F
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