Estimating Area Under Curves

Calculating derivatives

Finding the slope of a line

Estimating area under a curve using midpoint Riemann sum

Solving quadratic equations

Because different types are used for different functions

Because it affects the calculation of derivatives

Because it is crucial for solving AP test problems correctly

Because it determines the method of integration

From 0 to 5

From 2 to 13

From 3 to 15

From 1 to 10

Five

Four

Three

Two

Calculating the area

Using vertical dotted lines

Plotting the function

Drawing horizontal lines

(4, 15)

(3, 20)

(2, 5)

(6.5, 10)

To calculate the derivative

To determine the maximum value

To find the slope

To visualize the function f(x)

Base times height

Base divided by height

Base minus height

Base plus height

4

5

2

3

By using the endpoints of the interval

By using the midpoint of each interval

By using the average of the interval

By using the maximum value of the interval