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#