5.3: The Fundamental Theorem of Calculus

Hey guys, this is a brief update on the Fundamental Theorem of Calculus. We learned the first part of it in the previous section, which is:

If f is continuous on [a,b], then the function g defined by

is continuous on [a,b] and differentiable on (a,b) and g'(x) = f(x).

The Fundamental Theorem of Calculus Part II is as follows:

where F is the antiderivative of f so that F' = f.

Let's try a problem now, shall we?

So substitute 0 for a and (pi/2) in for b.

so the area of the graph is pi^2 +5.



sophie, i believe you are next up.