Riemann Sums and Graph Analysis

This video tutorial covers practice problems involving Riemann sums. It begins with an introduction on how to effectively use the practice problems. The video then presents four examples: calculating a left-hand Riemann sum, using a midpoint Riemann sum for a polynomial, determining displacement from a velocity table, and finding the signed area under a piecewise function. Each example is explained step-by-step, highlighting the calculation process and the interpretation of results. The video concludes with a summary and an invitation for feedback.

What is the best way to use the practice problem videos according to the introduction?

• Watch the video without pausing.

• Try each problem on your own first.

• Skip to the solutions immediately.

• Only watch the explanation part.

In the first problem, what is the function f(x) used for the left-hand Riemann sum?

• f(x) = cos(3x/2)

• f(x) = sin(3x/2)

• f(x) = 3x/2

• f(x) = tan(3x/2)

How many sub-intervals are used in the first problem's left-hand Riemann sum?

• 8

• 10

• 6

• 4

What is the value of delta x in the first problem?

• pi/3

• pi/4

• pi/8

• pi/6

In the second problem, what type of Riemann sum is used?

• Right-hand

• Trapezoidal

• Midpoint

• Left-hand

What is the polynomial function used in the second problem?

• 1/2 x^3 - 3x - 1

• x^3 + 3x - 1

• 1/2 x^2 - 3x - 1

• x^3 - 3x + 1

How many sub-intervals are used in the second problem's midpoint Riemann sum?

• 3

• 2

• 4

• 5

In the problem involving a table of values, what is the interval for the Riemann sum?

• 0 to 8

• 0 to 6

• 0 to 4

• 0 to 10

How many sub-intervals are used in the problem with the table of values?

• 3

• 2

• 4

• 5

In the final example, what type of function is used from 4 to 7?

• Quadratic

• Logarithmic

• Exponential

• Linear