Question

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

Answer 1

`f(x) = x^3/3 - (3 x^2) / 2 - 2x + 11/6`

Explanation:

Let's first solve the integral:

# int x^2 - 3x - 2 dx = int x^2 dx - 3 int x dx - 2 int 1 dx = x^3/3 - (3 x^2) / 2 - 2x + C #

We know that `f(-1) = 2`. Therefore, we set `x = -1` and solve the following equation:

`- 1/3 -3/2 + 2 + C = 2`.

Solving this, we find that `C = 11/6`, and thus

`f(x) = x^3/3 - (3 x^2) / 2 - 2x + 11/6`.