Suppose we have a function defined on the interval whose antiderivative is .
If and then how does one determine the value of ?
Thanks!
The way you have given it here, you can't determine C. But I suspect that is not what you mean to say. If the anti-derivative of f(x) is F(x)+ C, then you already know F(x) so already know both and and that tells you nothing about C. For example, I know that the anti-derivative of is so I know that and . That tells me nothing about C.
I think what you mean to say is that you know that , evaluated at , is (and you only need one value, not two). In that case, you have that so that . Using the example above, if you know that , evaluated at is K then so . More specifically, if you know that the anti-derivative of , evaluated at x= 2 is 12, then you know that so that .