Simpson's Rule and Average Speed

The video tutorial explains how to use Simpson's Rule to estimate the value of definite integrals. It covers the formula, calculation of delta x, and application of the rule to an example. The tutorial also demonstrates integration to verify results and solves a word problem involving car displacement and average speed using Simpson's Rule.

What is the primary purpose of using Simpson's Rule?

• To find the exact value of a definite integral

• To calculate the derivative of a function

• To approximate the value of a definite integral

• To solve differential equations

In the context of Simpson's Rule, what does delta x represent?

• The height of the rectangles

• The width of the rectangles

• The area under the curve

• The number of intervals

What is the function used in the example to apply Simpson's Rule?

• x squared

• x to the fifth

• x cubed

• x to the fourth

How does the result of Simpson's Rule compare to the exact integral in the example?

• Both give the same value

• Simpson's Rule gives a lower value

• The exact integral is not calculated

• Simpson's Rule gives a higher value

What is the interval used for calculating the car's displacement using Simpson's Rule?

• 0 to 10 minutes

• 0 to 20 minutes

• 0 to 30 minutes

• 0 to 40 minutes

How many sub-intervals are used in the car velocity problem?

• 4

• 5

• 6

• 7

What is the displacement of the car in the first 30 minutes?

• 50,600 meters

• 60,500 meters

• 40,600 meters

• 30,500 meters

How is the average speed of the car calculated?

• Total distance times total time

• Total distance divided by total time

• Average velocity times total time

• Total time divided by total distance

What is the average speed of the car for the entire trip?

• 27.6 meters per second

• 30.5 meters per second

• 28.1 meters per second

• 29.0 meters per second

How does the average speed compare to the average velocity calculated from the table?

• Both are the same

• Average speed is lower

• Average velocity is not calculated

• Average speed is higher