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#
