What is f(x) = int 3x^2-4 dx if f(2) = 2 ?
1 Answer
Jan 17, 2016
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(2)=2^3-4(2)+C=2
8-8+C=2
C=2
Thus,
f(x)=x^3-4x+2