What is f(x) = int -x^2+x-4 dxf(x)=∫−x2+x−4dx if f(2) = -1 f(2)=−1?

1 Answer
Pitufox27
Oct 10, 2016

We must evaluate the primitive and then substitute xx value to obtain - 1−1. 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 + Cf(x)=∫(−x2+x−4)dx=−13x3+12x2−4x+C

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

f (2) = - 1/3 (2)^3 + 1/2 (2)^2 - 4 (2) + C = - 1f(2)=−13(2)3+12(2)2−4(2)+C=−1

Thus:

- 8/3 + 2 - 8 + C = -1 rArr C = 23/3−83+2−8+C=−1⇒C=233

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