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

1 Answer
Aug 24, 2016

f(x)=3x^3-23

Explanation:

The first step is to simplify the expression to be integrated.

(3x+1)^2-6x-1=9x^2+6x+1-6x-1=9x^2

rArrint9x^2dx

integrate using color(blue)"power rule for integration"

color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(intax^n dx=a/(n+1)x^(n+1))color(white)(a/a)|)))

rArrint9x^2dx=9/3x^3+c=3x^3+c" c is a constant"

Using f(2) = 1 allows c to be calculated.

3(2)^3+c=1rArr24+c=1rArrc=-23

rArrf(x)=3x^3-23