Hello everyone.
I'm studying to my final Calculus 2 exam.
One of the theorems I have to know is the one mentioned in the title:
Let f : [a, b] -> R s.t. f is continuously differentiable then f is integrable
Now, I look for some intuition for this theorem - why is a function integrable if it's continuously differentiable?
Why Differentiability itself isn't sufficient? And therefore what is special in being continuously differentiable for a function to be integrable?
Thanks in advance.
I'm studying to my final Calculus 2 exam.
One of the theorems I have to know is the one mentioned in the title:
Let f : [a, b] -> R s.t. f is continuously differentiable then f is integrable
Now, I look for some intuition for this theorem - why is a function integrable if it's continuously differentiable?
Why Differentiability itself isn't sufficient? And therefore what is special in being continuously differentiable for a function to be integrable?
Thanks in advance.