What is f(x) = int (3x-2)^2-5x+1 dx if f(2) = 1 ?

1 Answer
May 29, 2016

f(x)=3x^3-17/2 x^2+5x+1

Explanation:

The indefinite integral is

int ((3x-2)^2-5x+1)\ dx=int (9x^2-17x+5)\ dx

=3x^3-17/2 x^2+5x+C

Therefore, f(x)=3x^3-17/2 x^2+5x+C for some C. Since f(2)=1, we must choose the value of C so that 1=3*2^3-17/2 * 2^2+5*2+C. This implies that 1=24-34+10+C so that C=1.

Hence, the answer is f(x)=3x^3-17/2 x^2+5x+1.