(4x)'= 4 andmaster1425 said:Homework Statement
Find the antiderivative F of f that satisifies the given condition. Check by comparing the graphs of f and F.
f(x)=4-3(1+x^2)^-1
F(1)=0
Homework Equations
The Attempt at a Solution
So far what I attempted to do was this:
F(x)=4x -3tan^-1(x) + C
but was unsure from here on.
An antiderivative is the reverse operation of a derivative. It is a function that, when differentiated, results in the original function.
Finding the antiderivative allows us to determine the original function from its derivative. This is useful in many scientific and mathematical applications, such as finding the position of an object from its velocity function.
To find the antiderivative of a function, you can use integration techniques such as the power rule, substitution, or integration by parts. These techniques involve manipulating the function algebraically to find a new function that, when differentiated, results in the original function.
An indefinite antiderivative is the general solution to an antiderivative problem, while a definite antiderivative is a specific solution that includes limits of integration. Indefinite antiderivatives are represented by the constant "C" while definite antiderivatives do not have a constant term.
Not all functions have antiderivatives. Some functions may have antiderivatives that cannot be expressed in terms of elementary functions, while others may not have antiderivatives at all. These functions are called non-integrable or non-elementary functions.