Question

What is `f(x) = int -x^2+x-4 dx` if `f(2) = -3`?

Answer 1

`y=-1/3x^3+1/2x^2-4x+17/3`

Explanation:

Integrate each term using the `color(blue)"power rule"`

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

`rArrint(-x^2+x-4)dx`

`y=-1/3x^3+1/2x^2-4x+c`

To find c, the constant of integration, substitute x = 2 , y = - 3

`rArr-1/3(2)^3+1/2(2)^2-4(2)+c=-3`

`rArrc=-3+8/3-2+8=5 2/3=17/3`

`rArry=-1/3x^3+1/2x^2-4x+17/3`