Numerical Integration and the Trapezoid Rule

This video tutorial explains numerical integration using the trapezoid rule with eight trapezoids. It covers the formula, coefficients, and provides a visual demonstration using Wolfram. The example calculation is set up with specific values, and function values are calculated using a graphing calculator. The tutorial emphasizes understanding the pattern of coefficients and the approximation process.

What is the purpose of using the trapezoid rule in numerical integration?

• To calculate derivatives

• To solve differential equations

• To find the exact value of an integral

• To approximate the value of a definite integral

How many trapezoids are used in this example to approximate the integral?

• 4

• 6

• 8

• 10

What is the pattern of coefficients in the trapezoid rule?

• First coefficient is 2, others are 1

• All coefficients are 2

• First and last coefficients are 1, others are 2

• All coefficients are 1

What is the value of delta x in this example?

• 1.0

• 0.5

• 2.0

• 0.25

What is the first x value (x0) in the list of x values?

• 2

• 1

• 3

• 0

What is the formula used to calculate the approximate integral using the trapezoid rule?

• b - a divided by 3n

• b - a divided by 2n

• b - a divided by n

• b - a divided by 4n

Which function is used in the integrand for this example?

• cosine x divided by x

• log x divided by x

• sin x divided by x

• tan x divided by x

What mode should the graphing calculator be in to find the function values?

• Gradient mode

• Radian mode

• Decimal mode

• Degree mode

What is the approximate value of the integral using the trapezoid rule with n equals eight?

• 0.4953

• -0.4953

• 0.5403

• -0.5403

How many decimal places are preferred for accuracy in this example?

• Three

• Two

• Four

• Five