5.3 The Fundamental Theorem of Calculus Part II

Fundamental Theorem of Calculus Part II

If f is a continuous function on [a,b] then

where F is any antiderivative of f, that is, a function such that F'=f.

Once you find the antiderivative of f(x), you evaluate the end points from a to b and then subtract the antiderivative function.

Lets look at an example.

Once you find the antiderivative, you plug the top number 5 into x and subtract that antiderivative function from an antiderivative function with the number 3 in x.



You can check your answer by using your calculator.
Plug into your calculator.
Go back to the home page. Click Math then 9.
Once fnInt pops up, put fnInt( ,X,3,5). You will get 98/3


Try this problem!




You will see that this antiderivative is:


Thus you plug in 4 into the x and then subtract the antiderivative with 2 in the x value.



This a reminder to Brian to do the next blog!

This website can help out with this concept:
http://math.ucsd.edu/~wgarner/math10b/ftc.htm


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