What is #f(x) = int 3x-4 dx# if #f(2) = 2 #?
1 Answer
Feb 12, 2016
# f(x) = 3/2 x^2 - 4x + 4#
Explanation:
using
# int ax^n dx = (ax^(n+1))/(n+1) + c # this is standard integral where c is the constant of integration
then
# int(3x - 4 ) dx = 3/2 x^2 - 4x + c # f(2) = 2 , allows c , to be found
hence :
# 3/2 .4 - 4(2) + c = 2 # 6 - 8 + c = 2 → c = 4
#rArr int(3x - 4)dx = 3/2 x^2 - 4x + 4 #
