The discussion revolves around understanding the arguments of functions within the context of indefinite integrals, specifically focusing on examples like \(\cos(x^2)\) and \(e^{\tan(x)}\). Participants are exploring how to identify the arguments of these functions and their implications for integration.
The conversation is ongoing, with participants providing insights into the structure of the functions and raising questions about integrating multiple functions. There is no explicit consensus yet, as the discussion is still exploring different interpretations.
Participants are considering the implications of integrating functions with different arguments and the potential complexity that arises when both functions are involved. There is an emphasis on understanding the arguments without providing a definitive method for integration.
What if both functions are to be integratedBvU said:Hi,
Both are examples of the kind ##f\left( g(x)\right)\ ##.
The argument for ##f()##, the cosine function ##\cos()##, is ##x^2##, so ##g(x) = x^2##.
Similarly, the argument for exponentiation ## f() = \exp() \ ## is ##g(x) = \tan(x)##.
The integrand in both cases is ##f##, so you integrate ##\int f(g(x)) \, dx ##
If both functions are to be integrated what is the argument to integrate?BvU said:Hi,
Both are examples of the kind ##f\left( g(x)\right)\ ##.
The argument for ##f()##, the cosine function ##\cos()##, is ##x^2##, so ##g(x) = x^2##.
Similarly, the argument for exponentiation ## f() = \exp() \ ## is ##g(x) = \tan(x)##.
The integrand in both cases is ##f##, so you integrate ##\int f(g(x)) \, dx ##
? Can you write the form of the integral that you mean ?Michael Santos said:What if both functions are to be integrated