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

1 Answer
Oct 10, 2016

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