Lesson 2: 5.2 The Definite Integral

How can we find the exact area under a curve?
How can we turn our previous estimations for area under a curve into exact answers?

- sigma summation
- integral
- definite integral
- limits of integration
- midpoint rule

(calculating exact area under a curve)

- Using a definite integral to calculate the exact area under a curve
- 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 usually understand the application of the limit in order to extend our estimate with a fixed number of rectangles to infinite rectangles, which leads to a solid understanding of the initial setup of the formula for exact area under a curve. Where they often get tripped up in this section is the algebra between the initial setup and simplifying to an answer.

Homogeneous grouping and whole-class discussion

section assessment

problems assigned from book