Riemann Sums And Trapezoid Methods

Question 1

What is a Riemann Sum?

Answer 1

Approximation of the area under a curve using area of rectangles.

Question 2

What does the Right Riemann Sum use to determine height?

Answer 2

The right side of a rectangle

Question 3

What is the formula for Right Riemann Sum?

Answer 3

Distance between 2 x-values * right y-value (height).

Question 4

When is the right Riemann sum an UNDER-estimate?

Answer 4

When f’(x) is negative
(Sloping down)

Question 5

When is the Right Riemann sum an OVER-estimate

Answer 5

When f’(x) is positive
(Sloping up)

Question 6

What does the Left Riemann Sum use to determine height?

Answer 6

The left side of a rectangle

Question 7

What is the formula for Left Riemann Sum?

Answer 7

Distance between 2 x-values * left y-value (height).

Question 8

When is the Left Riemann Summit an OVER-estimate?

Answer 8

When f’(x) is negative
(Sloping down)

Question 9

When is the Left Riemann Sum an UNDER-estimate

Answer 9

When f’(x) is positive
(Sloping up)

Question 10

What tip can help visualize the Right Riemann Sum?

Answer 10

Turn the table on its side; the numbers used will form an ‘R’.

Question 11

What tip can help visualize the Left Riemann Sum?

Answer 11

Turn the table on its side; the numbers used will form an ‘L’.

Question 12

What are Riemann Sums used for?

Answer 12

To approximate area under a curve
∫ f(x) dx