Worked example: finding a Riemann sum using a table | AP Calculus AB | Khan Academy

TL;DR

Use a right Riemann sum with three equal subdivisions to approximate the area between the x-axis and a function graph.

Transcript

• [Tutor] Imagine we're asked to approximate the area between the x-axis and the graph of f from x equals one to x equals 10 using a right Riemann sum with three equal subdivisions. To do that, we are given a table of values for f, so I encourage you to pause the video and see if you can come up with an approximation for the area between the x axis... Read More

Key Insights

• 🗯️ A right Riemann sum can be used to estimate the area under a function graph using a table of values.
• 🗯️ The height of each rectangle in a right Riemann sum is determined by the value of the function at the right boundary of the subdivision.
• #️⃣ The accuracy of the approximation depends on the number of subdivisions and the behavior of the function.
• 🍹 The area under the curve can be estimated by summing the areas of the rectangles in the right Riemann sum.
• 💁 The approximation may not be exact due to the limited information provided by the table of values.
• ↔️ The right Riemann sum is based on the right boundary of each subdivision, unlike the left Riemann sum which uses the left boundary.
• 🗯️ By visualizing the graph, it becomes easier to understand the concept of the right Riemann sum.

Questions & Answers

Q: What is a right Riemann sum used for?

A right Riemann sum is used to approximate the area between the x-axis and a function graph by dividing the interval into subdivisions and using the right boundary of each subdivision as the height of the rectangle.

Q: How many subdivisions are used in a right Riemann sum with three equal subdivisions?

In a right Riemann sum with three equal subdivisions, the interval is divided into three sections, each of equal width.

Q: How are the heights of the rectangles determined in a right Riemann sum?

In a right Riemann sum, the height of each rectangle is determined by the value of the function at the right boundary of the corresponding subdivision.

Q: Can an approximation using a right Riemann sum be used to determine the exact area under the curve?

No, the approximation using a right Riemann sum only provides an estimate of the area. The accuracy of the approximation depends on the behavior of the function and the number of subdivisions used.

Summary & Key Takeaways

• Given a table of values for a function f, we can still approximate the area between the x-axis and the graph using a right Riemann sum with three equal subdivisions.

• The right Riemann sum uses the right boundary of each subdivision as the height of the corresponding rectangle.

• By summing the areas of these rectangles, we can estimate the area under the curve.