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

1 Answer
Feb 12, 2016

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