1. Bellringer -- Numerical Word Search (in groups)
2. The Fundamental Theorem of Calculus
Each branch of mathematics has a fundamental theorem associated with it.
The Fundamental Theorem of Arithmetic:
Any positive integer can be represented in exactly one way as a product of primes.
The Fundamental Theorem of Algebra:
Every polynomial of degree n has exactly n zeros.
The Fundamental Theorem of Geometry:
No theorem wears this title, but perhaps the Pythagorean Theorem deserves it.
The Fundamental Theorem of Calculus — there are actually two parts to this theorem:
The First Fundamental Theorem of Calculus:
The derivative of the integral of a function is equal to the function.
The Second Fundamental Theorem of Calculus:
The integral of the derivative of a function is is equal to the function evaluated at its endpoints.
The F.T.C. tells us that we can evaluate a definite integral by taking an indefinite integral and substituting in the endpoints and taking the difference:
Remember that you can't spell FUNDAMENTAL without FUN (and MENTAL, and DA). So, think of The Fundamental Theorem of Calculus as DA MENTAL FUN.
3. Examples:
4. Properties of the Definite Integral
5. Examples of the Properties of the Definite Integral
