What is f(x) = int (3x-1)^2-2x+1 dx if f(2) = 1 ?

1 Answer
Jan 21, 2016

f(x)=3x^3-4x^2+2x-11

Explanation:

Now, the given function is apparently an integral of another function.
That is f(x)=int((3x-1)^2-2x+1)dx
Before integrating, let's expand and simplify the terms shall we?

(3x-1)^2-2x+1=9x^2+1-6x-2x+1=9x^2-8x+2
So, int(9x^2-8x+2)dx=9x^3/3-8x^2/2+2x+c
\impliesf(x)=3x^3-4x^2+2x+c

Given that at x=2" "f(x)=1
So, 3*2^3-4*2^2+2*2+c=1\implies3*8-4*4+4+c=1
:.24-16+4+c=1\impliesc=-11
Substituting for c we get the answer I have written above.