How do I evaluate constants of integration?

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Answer 1 · 2014-10-17T19:49:46

If $G (x)$ $G(x)$ is an antiderivative of $f (x)$ $f(x)$ and $G (x_{0}) = y_{0}$ $G(x_0)=y_0$ , then

$G (x) = \int f (x) d x = F (x) + C$ $G(x)=int f(x)dx=F(x)+C$ ,

where $F (x)$ $F(x)$ is any antiderivative of $f (x)$ $f(x)$ .

Since

$G (x_{0}) = F (x_{0}) + C = y_{0}$ $G(x_0)=F(x_0)+C=y_0$ ,

we have

$C = y_{0} - F (x_{0})$ $C=y_0-F(x_0)$ .

I hope that this was helpful.