Question

What is `f(x) = int 3x-4 dx` if `f(2) = 2`?

Answer 1

`f(x) = 3/2 x^2 - 4x + 4`

Explanation:

using `int ax^n dx = (ax^(n+1))/(n+1) + c`

this is standard integral where c is the constant of integration

then `int(3x - 4 ) dx = 3/2 x^2 - 4x + c`

f(2) = 2 , allows c , to be found

hence : `3/2 .4 - 4(2) + c = 2`

6 - 8 + c = 2 → c = 4

`rArr int(3x - 4)dx = 3/2 x^2 - 4x + 4`