High School Calculus/The Fundamental Theorems of Calculus
The Fundamental Theorems of Calculus
In order to understand the fundamental theorem of calculus we must first understand what an Antiderivative is.
An antiderivative is denoted by F.
Let's do some practice on this
If you differentiate this problem you will end up with
Essentially what is happening is this
When dealing with functions that have a plus or minus in them you can integrate the separately to help you out and really focus on what is going on. With enough practice you won't need to do this. Remember to keep the appropriate sign between the integrals.
What was done here was a constant multiplier was pulled out. When you have a common constant multiplier in a function, you can pull it out of the integral to make it easier to evaluate. Just don't forget to multiply it back in when you are done.