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 #
