Question

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

Answer 1

`f(x)=-1/4x^4+3/2x^2-4x+3`

Explanation:

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

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(int(ax^n)=a/(n+1)x^(n+1) ; n≠-1)color(white)(2/2)|)))`

`rArrint(-x^3+3x-4)dx`

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

`"solve for c, given "f(2)=-3`

`-3=-4+6-8+crArrc=3`

`rArrf(x)=-1/4x^4+3/2x^2-4x+3`