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

1 Answer
Jan 17, 2016

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

Explanation:

First, find the antiderivative of the function using the product rule in reverse:

intax^ndx=(ax^(n+1))/(n+1)+C

Thus,

f(x)=(3x^(2+1))/(2+1)-(4x^(0+1))/(0+1)+C=(3x^3)/3-(4x)/1+C=x^3-4x+C

Since f(x)=x^3-4x+C, and we know that f(2)=2, we can determine C (the constant of integration).

f(2)=2^3-4(2)+C=2

8-8+C=2

C=2

Thus,

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