Understanding the Area Between Two Curves

The length of the curve

The slope of the function

The area under the curve

The volume of the solid

The function that is below the other on the graph

The function that is above the other on the graph

The function with the lower degree

The function with the higher degree

(0, 0) and (3, 6)

(2, 4) and (5, 10)

(1, 1) and (3, 9)

(0, 0) and (4, 8)

By choosing any two points on the x-axis

By finding the points of intersection of the curves

By using the maximum and minimum values of the functions

By selecting the endpoints of the interval

Setting the functions equal to zero

Determining the maximum value of the functions

Finding the points of intersection

Calculating the derivative of the functions

16/3

32/3

64/3

48/3

It allows for the use of a single integral

It simplifies the calculation by doubling one area

It eliminates the need for integration

It changes the limits of integration

-1, 0, and 1

-3, 0, and 3

-2, 0, and 2

0, 1, and 2

Because the functions are linear

Because the functions intersect at more than two points

Because the functions are quadratic

Because the functions are not continuous

10 square units

8 square units

6 square units

4 square units