Lesson 3: 5.3 The Fundamental Theorem of Calculus
Duration of Days: 4
Lesson Objective
Students will be able to make the connection that integration and derivatives are inverse processes (the FTC) and apply this to integrals.
- How are derivatives and integrals related?
- How can we use the FTC to make integration simpler?
- What happens when we take the derivative of an integral function? Or when we integrate a derivative function?
- The Fundamental Theorem of Calculus
- anti-derivative
(Using anti-derivatives to solve integrals)
Make the connection that derivatives and integrals are inverse processes, and to apply that concept by using anti-derivatives to solve integrals.
DOK levels 1-4
- calculation of total revenue or cost over time
- probabilities in statistics for continuous random variables
- population growth, radioactive decay
- filtering and analyzing data signals in electronics
- calculation of exact volumes or surface areas of irregular shapes
Students often will be confused on the problems that ask them to take the derivative of a function that is itself an integral. They feel the need to solve the integral, when they really just need to recognize that taking the derivative cancels the integral, leaving essentially the original function inside the integral.
homogeneous grouping and whole-class discussion
section assessment
problems assigned from the book