What is f(x) = int (x-3)^2-3x+4 dx if f(2) = 1 ?

1 Answer
Jan 24, 2016

f(x) = x^3/3 -(9x^2)/2 +13x -29/3

Explanation:

First, expand the integrant as follow

int((x-3)^2 -3x +4)dx = int(x^2-6x+9-3x+4)dx

=int(x^2-9x+13)dx

Then we can integrate this using the power rule like this

f(x) = x^3/3-(9x^2)/2+13x+C#

We are given f(2) = 1 , substitute this into the f(x) to solve for C

1= (2^3)/3-(9(2)^2)/2+13(2) +C

1= 8/3 -36/2 +26+C

1= 8/3 -18 +26+C

C= -29/3

So f(x) = x^3/3 -(9x^2)/2 +13x -29/3