The Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus says that to calculate a definite integral of f(x), you can use any antiderivative, F(x), of f(x). Specifically:
This applet helps you explore this very important mathematical theorem.
On the left is the definite integral of f(x) from a to b shaded red.
On the right is an antiderivative, F(x), of f(x), and the difference F(b)-F(a), also shaded red.
The Fundamental Theorem of Calculus (amazingly) says that these two numbers are equal. There is not an immediately obvious reason why these two numbers are equal. Nonetheless, these two numbers are equal.
You can explore by making changes in the app.
In the left pane you can change:
- f(x)
- a
- b