1.3.2 The Fundamental Theorem of Calculus

Section 1.3.2 of Electromagnetism by Griffiths

Mathematically describe the fundamental theorem of calculus.

Describe the fundamental theorem of calculus.

It tells you how to integrate F(x): you think up a function f(x) whose derivative is equal to F.

What is the geometrical interpretation of the fundamental theorem of calculus?

If you chop the internal from a to b into many tiny pieces, dx, and add up the increments df from each little piece, the result is equal to the total change in f: f(b) - f(a)

What is the basic format of the fundamental theorem of calculus?

The integral of a derivative over some region is given by the value of the function at the end points (boundaries).

What are the fundamental theorems corresponding to the three species of derivative in vector calculus?

The gradient, divergence, and curl all have their own fundamental theorems.