INTEGRATION
Antiderivates
A fucntion F is an antiderivative of f on an interval I if F'(x) = f(x) for all x in I.
There are many antiderivates for such equation f because of the constants that can be present in the function. Therefore, one must add a + C to the end of the antiderivative for any constant, C.
Solving a Differential Equation
Given y’ = 2x, find the general solution of the differential equation.
The antiderivative of y’ = 2x is y = x^2. This can be solved by using one of the Basic Integration Rules. Specifically #4 on this list:
Here are a few examples of Integrating/Antiderivatives and using the Rewriting technique before integrating:
Calculus Corner 