How do I evaluate constants of integration?

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Answer 1 · 2014-10-17T19:49:46

If #G(x)# is an antiderivative of #f(x)# and #G(x_0)=y_0#, then

#G(x)=int f(x)dx=F(x)+C#,

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

Since

#G(x_0)=F(x_0)+C=y_0#,

we have

#C=y_0-F(x_0)#.

I hope that this was helpful.