I have moved this thread, as it is not a precalculus problem.beyondlight said:Homework Statement
Determine all primitive functions for the function:
2x(x^2+3)^4
2. The attempt at a solution
When i expanded i got the primitive to be:
2(x^9/9)+3x^8+18x^6+54x^4+81x^2But this was wrong. I am not sure I have understood the question. Help?
If z = x^2 + 3, what is dz?beyondlight said:One possible substitution is 2x(z)^4
A very simple substitution will work, and you're on the right track,beyondlight said:But I am not sure how to proceed from here...
A primitive function is a fundamental function that cannot be further simplified or decomposed into simpler functions. It is the most basic form of a function and is often used as a starting point for more complex functions.
To determine all primitive functions, you need to use the process of integration. This involves finding the antiderivative of a given function, which is the function that, when differentiated, gives the original function. The set of all antiderivatives is equivalent to the set of all primitive functions.
No, not all functions have primitive functions. Only continuous functions have primitive functions. Discontinuous functions or functions with discontinuities at certain points do not have primitive functions.
To find the primitive function of a specific function, you can use techniques such as integration by parts, substitution, or partial fractions. These techniques help you manipulate the given function to find its antiderivative, which is the primitive function.
Primitive functions are important because they allow us to solve complex problems involving derivatives and integrals. They also help us understand the behavior and properties of functions. In addition, primitive functions have many practical applications in fields such as physics, engineering, and economics.