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