The problem involves finding the antiderivative of the function f(x) = 4 - 3(1 + x^2)^-1, with the condition that F(1) = 0. Participants are tasked with checking their work by comparing the graphs of f and F.
Some participants are seeking confirmation on their derived expressions for F(x) and are exploring the implications of the condition F(1) = 0. There is a mix of attempts to clarify the differentiation of their expressions and to solve for the constant C.
Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is a focus on ensuring the correctness of their antiderivative and the associated conditions.
(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.