Question

How do you find the antiderivative of `f(x)=4x^2-6x+7`?

Answer 1

`int f(x) dx = 4/3x^3-3x^2+7x+C`

Explanation:

`f(x) = 4x^2-6x+7`

`int f(x) dx = int (4x^2-6x+7)dx`

`= 4*int x^2 dx -6* int xdx+7* int 1dx`

Applying the power rule to each term:

`= (4x^3)/3 - (6x^2)/2 +(7x^1)/1 +C`

`= 4/3x^3-3x^2+7x+C`