Question

What is `f(x) = int -x^2+x-4 dx` if `f(2) = -1`?

Answer 1

We must evaluate the primitive and then substitute `x` value to obtain `- 1`. This becomes a first degree equation over C and we can obtain the value of the constant of integration.

Explanation:

First we solve the primitive:

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

Then, if `f(2)=- 1`, substituing the x value in the expression of the primitive and equals to the `f (x)` value, we obtain:

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

Thus:

`- 8/3 + 2 - 8 + C = -1 rArr C = 23/3`