Lesson 1: 6.1 Areas Between Curves

- What types of rectangles should be used, vertical or horizontal?
- Which curve is the "upper" and which is the "lower"?
- How do we find the intersection points?
- What variable will our integral be in terms of?

- enclosed region
- vertical/horizontal rectangles

(finding area between two curves)

Determine the area between two curves.
DOK levels 1-4

- consumer or producer surplus in economics
- Calculating the cross-sectional area of complex, non-linear components to determine volume, material usage, or structural strength, such as designing arch bridges or building structural beams.
- Finding the net work done by a force over a distance by calculating the area between a variable force curve and a displacement axis, or measuring net energy in a system.

Students may mix x's and y's in the same integral without solving an equation to be in terms of the variable needed.
Students also can have difficulty visualizing graphs without the aid of a graphing device.

Homogeneous grouping and whole-class discussion

section assessment

problems assigned from book