What is f(x) = int -x^2-4 dx if f(2) = -1 ?
1 Answer
Feb 7, 2016
f(x) = -1/3 x^3 - 4x + 29/3
Explanation:
intax^n dx =( ax^(n+1))/(n+1) + c : n ≠ -1
where c , is the constant of integration , is the standard integral.apply this to each 'term by term'
hence
int(-x^2 - 4 )dx = -1/3 x^3 - 4x + c using f(2) = - 1 , allows c to be calculated.
hence :
-1/3 (2)^3 - 4(2) + c = - 1
-8/3 - 8 + c = - 1 rArr c = -1 + 8 + 8/3 rArr c = 29/3
