`f(x) = x - 3` Find the most general antiderivative of the function. (Check your answer by differentiation.)

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Chapter 4, 4.9 - Problem 1 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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lemjay | High School Teacher | (Level 3) Senior Educator

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`f(x) = x - 3`

To find the general antiderivative of this function, we take its integral.

`F(x) = int f(x) dx = int(x-3)dx`

Take the integral of each term.

`=intxdx - int3dx`

For the first integral, apply the formula `int u^n=du = u^(n+1)/(n+1) + C` .

And for the second integral,  apply the formula `int cdu= cu + C.`

`=x^2/2-3x + C`

(where C represents a constant.)

Therefore, the antiderivative of `f(x) =x - 3`   is   `F(x) =x^2/2-3x+C` .

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