What is f(x) = int (3x+1)^2-6x+1 dx if f(2) = 1 ?

1 Answer
May 17, 2018

3x^3+2x-27

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