Question about functions

[member 392791]

Hello,

I am curious, suppose I have a function of x, f(x). Suppose I also have another function P(x). Does this mean I am allowed to have f(P) and I can do standard methods of integration and such on it?

 

[Robert1986]

If P is the variable that you are integrating. For example, $\int \sin(x^2) d(x^2)$ can be computed the way it seems you want to compute it. That is, $\int \sin(x^2) d(x^2) = - \cos(x^2)$. However, $\int \sin(x^2) dx \neq - \cos(x^2)$. The question you are asking has a lot to do with the integration method known as "u-substitution." Do you know what that is?