# Intuition: Fundamental Theorem of Calculus

- Author:
- Joqsan

- Topic:
- Calculus, Definite Integral

I just wanted to have a visual intuition on how the Fundamental Theorem of Calculus works. Maybe it's not rigorous, but it could be helpful for someone (:.
I've used the concepts of velocity, distance and time because, I think, they are the ones with which we are more familiarized and also used them to write one part of the theorem (is it illegal?).

**INSTRUCTIONS (:**:- Plug in any function you want in the input box
**v(t)**. Make sure that the variable you're using is**t**instead of**x**, though.

- Choose your own interval by moving the points
**a**and**b**along the x axis.

- The general form of an antiderivative is
**a + C**, where**C**is a constant. Move the slider ''Constant'' to shift the position of**d(t)**along the y axis. The slider has two purposes:- It allows you to move
**d(t)**when it overlaps with**v(t)**, so that the visualization doesn't get messy. - It shows you that changing the constant
**C**doesn't change the difference**d(b) - d(a)**: A neat way to see how the Definite Integral of**v(t)**is connected to its infinitely many antiderivatives (Remember that the antiderivatives of a function just differ in**C**, the constant term).

- It allows you to move

- Check the box ''Riemann Sum'' and move the slider ''Rectangles'' to see how it approaches a Definite Integral as the number of rectangles goes to infinity (the slider doesn't go to infinity but up to 60 isn't that bad).