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

1 Answer
Dec 20, 2017

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.