What is f(x) = int (3x+1)^2-6x+1 dx if f(2) = 1 ?
1 Answer
May 17, 2018
Explanation:
"expand and simplify"
rArrint(9x^2+6x+1-6x+1)dx
=int(9x^2+2)dx
"integrate each term using the "color(blue)"power rule"
•color(white)(x)int(ax^n)=a/(n+1)x^(n+1)ton!=-1
rArrint(9x^2+2)dx=3x^3+2x+c
"where c is the constant of integration"
"to find c use "f(2)=1
rArr3(2)^3+2(2)+c=1
rArrc=1-28=-27
rArr3x^3+2x-27